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a| > r \\iff x \u003C a - r \\ \\text{ oder } \\ x > a + r",[568,1051,1053,1074,1095,1120,1139,1158,1194,1212],{"className":1052,"ariaHidden":612},[611],[568,1054,1056,1059,1062,1065,1068,1071],{"className":1055},[616],[568,1057],{"className":1058,"style":621},[620],[568,1060,590],{"className":1061},[625],[568,1063,593],{"className":1064},[625,629],[568,1066],{"className":1067,"style":634},[633],[568,1069,597],{"className":1070},[638],[568,1072],{"className":1073,"style":634},[633],[568,1075,1077,1080,1083,1086,1089,1092],{"className":1076},[616],[568,1078],{"className":1079,"style":621},[620],[568,1081,600],{"className":1082},[625,629],[568,1084,590],{"className":1085},[625],[568,1087],{"className":1088,"style":789},[633],[568,1090,1012],{"className":1091},[793],[568,1093],{"className":1094,"style":789},[633],[568,1096,1098,1102,1105,1108,1111,1114,1117],{"className":1097},[616],[568,1099],{"className":1100,"style":1101},[620],"height:0.549em;vertical-align:-0.024em;",[568,1103,746],{"className":1104,"style":806},[625,629],[568,1106],{"className":1107,"style":789},[633],[568,1109],{"className":1110,"style":789},[633],[568,1112,1020],{"className":1113},[793],[568,1115],{"className":1116,"style":789},[633],[568,1118],{"className":1119,"style":789},[633],[568,1121,1123,1127,1130,1133,1136],{"className":1122},[616],[568,1124],{"className":1125,"style":1126},[620],"height:0.5782em;vertical-align:-0.0391em;",[568,1128,593],{"className":1129},[625,629],[568,1131],{"className":1132,"style":789},[633],[568,1134,1027],{"className":1135},[793],[568,1137],{"className":1138,"style":789},[633],[568,1140,1142,1146,1149,1152,1155],{"className":1141},[616],[568,1143],{"className":1144,"style":1145},[620],"height:0.6667em;vertical-align:-0.0833em;",[568,1147,600],{"className":1148},[625,629],[568,1150],{"className":1151,"style":634},[633],[568,1153,597],{"className":1154},[638],[568,1156],{"className":1157,"style":634},[633],[568,1159,1161,1165,1168,1171,1179,1182,1185,1188,1191],{"className":1160},[616],[568,1162],{"className":1163,"style":1164},[620],"height:0.7335em;vertical-align:-0.0391em;",[568,1166,746],{"className":1167,"style":806},[625,629],[568,1169,894],{"className":1170},[633],[568,1172,1175],{"className":1173},[625,1174],"text",[568,1176,1178],{"className":1177},[625]," oder ",[568,1180,894],{"className":1181},[633],[568,1183,593],{"className":1184},[625,629],[568,1186],{"className":1187,"style":789},[633],[568,1189,1012],{"className":1190},[793],[568,1192],{"className":1193,"style":789},[633],[568,1195,1197,1200,1203,1206,1209],{"className":1196},[616],[568,1198],{"className":1199,"style":1145},[620],[568,1201,600],{"className":1202},[625,629],[568,1204],{"className":1205,"style":634},[633],[568,1207,899],{"className":1208},[638],[568,1210],{"className":1211,"style":634},[633],[568,1213,1215,1218],{"className":1214},[616],[568,1216],{"className":1217,"style":685},[620],[568,1219,746],{"className":1220,"style":806},[625,629],[564,1222,1223,1224,689,1252,1283,1284,1312,1313,1395],{},"Bei ",[568,1225,1227,1240],{"className":1226},[571],[568,1228,1230],{"className":1229},[575],[577,1231,1232],{"xmlns":579},[581,1233,1234,1238],{},[584,1235,1236],{},[595,1237,1027],{},[604,1239,1027],{"encoding":606},[568,1241,1243],{"className":1242,"ariaHidden":612},[611],[568,1244,1246,1249],{"className":1245},[616],[568,1247],{"className":1248,"style":1126},[620],[568,1250,1027],{"className":1251},[793],[568,1253,1255,1270],{"className":1254},[571],[568,1256,1258],{"className":1257},[575],[577,1259,1260],{"xmlns":579},[581,1261,1262,1267],{},[584,1263,1264],{},[595,1265,1266],{},"≥",[604,1268,1269],{"encoding":606},"\\geq",[568,1271,1273],{"className":1272,"ariaHidden":612},[611],[568,1274,1276,1280],{"className":1275},[616],[568,1277],{"className":1278,"style":1279},[620],"height:0.7719em;vertical-align:-0.136em;",[568,1281,1266],{"className":1282},[793]," ändern sich nur die Randpunkte. Ist ",[568,1285,1287,1300],{"className":1286},[571],[568,1288,1290],{"className":1289},[575],[577,1291,1292],{"xmlns":579},[581,1293,1294,1298],{},[584,1295,1296],{},[587,1297,746],{},[604,1299,746],{"encoding":606},[568,1301,1303],{"className":1302,"ariaHidden":612},[611],[568,1304,1306,1309],{"className":1305},[616],[568,1307],{"className":1308,"style":685},[620],[568,1310,746],{"className":1311,"style":806},[625,629]," negativ, hat ",[568,1314,1316,1341],{"className":1315},[571],[568,1317,1319],{"className":1318},[575],[577,1320,1321],{"xmlns":579},[581,1322,1323,1339],{},[584,1324,1325,1327,1329,1331,1333,1335,1337],{},[587,1326,590],{"mathvariant":589},[587,1328,593],{},[595,1330,597],{},[587,1332,600],{},[587,1334,590],{"mathvariant":589},[595,1336,743],{},[587,1338,746],{},[604,1340,749],{"encoding":606},[568,1342,1344,1365,1386],{"className":1343,"ariaHidden":612},[611],[568,1345,1347,1350,1353,1356,1359,1362],{"className":1346},[616],[568,1348],{"className":1349,"style":621},[620],[568,1351,590],{"className":1352},[625],[568,1354,593],{"className":1355},[625,629],[568,1357],{"className":1358,"style":634},[633],[568,1360,597],{"className":1361},[638],[568,1363],{"className":1364,"style":634},[633],[568,1366,1368,1371,1374,1377,1380,1383],{"className":1367},[616],[568,1369],{"className":1370,"style":621},[620],[568,1372,600],{"className":1373},[625,629],[568,1375,590],{"className":1376},[625],[568,1378],{"className":1379,"style":789},[633],[568,1381,743],{"className":1382},[793],[568,1384],{"className":1385,"style":789},[633],[568,1387,1389,1392],{"className":1388},[616],[568,1390],{"className":1391,"style":685},[620],[568,1393,746],{"className":1394,"style":806},[625,629]," keine Lösung, weil ein Betrag nie negativ ist.",[564,1397,1398,1399,1427,1428,1431],{},"Steht auf beiden Seiten ein Term mit ",[568,1400,1402,1415],{"className":1401},[571],[568,1403,1405],{"className":1404},[575],[577,1406,1407],{"xmlns":579},[581,1408,1409,1413],{},[584,1410,1411],{},[587,1412,593],{},[604,1414,593],{"encoding":606},[568,1416,1418],{"className":1417,"ariaHidden":612},[611],[568,1419,1421,1424],{"className":1420},[616],[568,1422],{"className":1423,"style":685},[620],[568,1425,593],{"className":1426},[625,629],", hilft die ",[656,1429,1430],{},"Fallunterscheidung",":",[1433,1434,1435,1486],"ol",{},[1436,1437,1438,1439,1485],"li",{},"Fall: Der Inhalt des Betrags ist ",[568,1440,1442,1460],{"className":1441},[571],[568,1443,1445],{"className":1444},[575],[577,1446,1447],{"xmlns":579},[581,1448,1449,1457],{},[584,1450,1451,1453],{},[595,1452,1266],{},[1454,1455,1456],"mn",{},"0",[604,1458,1459],{"encoding":606},"\\geq 0",[568,1461,1463,1475],{"className":1462,"ariaHidden":612},[611],[568,1464,1466,1469,1472],{"className":1465},[616],[568,1467],{"className":1468,"style":1279},[620],[568,1470,1266],{"className":1471},[793],[568,1473],{"className":1474,"style":789},[633],[568,1476,1478,1482],{"className":1477},[616],[568,1479],{"className":1480,"style":1481},[620],"height:0.6444em;",[568,1483,1456],{"className":1484},[625],". Betragsstriche einfach weglassen.",[1436,1487,1488,1489,1532],{},"Fall: Der Inhalt ist ",[568,1490,1492,1508],{"className":1491},[571],[568,1493,1495],{"className":1494},[575],[577,1496,1497],{"xmlns":579},[581,1498,1499,1505],{},[584,1500,1501,1503],{},[595,1502,1027],{},[1454,1504,1456],{},[604,1506,1507],{"encoding":606},"\u003C 0",[568,1509,1511,1523],{"className":1510,"ariaHidden":612},[611],[568,1512,1514,1517,1520],{"className":1513},[616],[568,1515],{"className":1516,"style":1126},[620],[568,1518,1027],{"className":1519},[793],[568,1521],{"className":1522,"style":789},[633],[568,1524,1526,1529],{"className":1525},[616],[568,1527],{"className":1528,"style":1481},[620],[568,1530,1456],{"className":1531},[625],". Betragsstriche durch eine Klammer mit Minus davor ersetzen.",[564,1534,1535],{},"In jedem Fall löst man die Ungleichung und schneidet das Ergebnis mit der Fallbedingung. Die Lösungsmenge ist die Vereinigung beider Fälle.",[559,1537,1539],{"id":1538},"beispiele","Beispiele",[564,1541,1542,1629,1630,1687,1688,689,1722,1750],{},[568,1543,1545,1576],{"className":1544},[571],[568,1546,1548],{"className":1547},[575],[577,1549,1550],{"xmlns":579},[581,1551,1552,1573],{},[584,1553,1554,1556,1559,1561,1563,1566,1568,1570],{},[587,1555,590],{"mathvariant":589},[1454,1557,1558],{},"2",[587,1560,593],{},[595,1562,597],{},[1454,1564,1565],{},"3",[587,1567,590],{"mathvariant":589},[595,1569,743],{},[1454,1571,1572],{},"5",[604,1574,1575],{"encoding":606},"|2x - 3| \\leq 5",[568,1577,1579,1601,1620],{"className":1578,"ariaHidden":612},[611],[568,1580,1582,1585,1589,1592,1595,1598],{"className":1581},[616],[568,1583],{"className":1584,"style":621},[620],[568,1586,1588],{"className":1587},[625],"∣2",[568,1590,593],{"className":1591},[625,629],[568,1593],{"className":1594,"style":634},[633],[568,1596,597],{"className":1597},[638],[568,1599],{"className":1600,"style":634},[633],[568,1602,1604,1607,1611,1614,1617],{"className":1603},[616],[568,1605],{"className":1606,"style":621},[620],[568,1608,1610],{"className":1609},[625],"3∣",[568,1612],{"className":1613,"style":789},[633],[568,1615,743],{"className":1616},[793],[568,1618],{"className":1619,"style":789},[633],[568,1621,1623,1626],{"className":1622},[616],[568,1624],{"className":1625,"style":1481},[620],[568,1627,1572],{"className":1628},[625],": Der Term ",[568,1631,1633,1653],{"className":1632},[571],[568,1634,1636],{"className":1635},[575],[577,1637,1638],{"xmlns":579},[581,1639,1640,1650],{},[584,1641,1642,1644,1646,1648],{},[1454,1643,1558],{},[587,1645,593],{},[595,1647,597],{},[1454,1649,1565],{},[604,1651,1652],{"encoding":606},"2x - 3",[568,1654,1656,1678],{"className":1655,"ariaHidden":612},[611],[568,1657,1659,1663,1666,1669,1672,1675],{"className":1658},[616],[568,1660],{"className":1661,"style":1662},[620],"height:0.7278em;vertical-align:-0.0833em;",[568,1664,1558],{"className":1665},[625],[568,1667,593],{"className":1668},[625,629],[568,1670],{"className":1671,"style":634},[633],[568,1673,597],{"className":1674},[638],[568,1676],{"className":1677,"style":634},[633],[568,1679,1681,1684],{"className":1680},[616],[568,1682],{"className":1683,"style":1481},[620],[568,1685,1565],{"className":1686},[625]," muss zwischen ",[568,1689,1691,1707],{"className":1690},[571],[568,1692,1694],{"className":1693},[575],[577,1695,1696],{"xmlns":579},[581,1697,1698,1704],{},[584,1699,1700,1702],{},[595,1701,597],{},[1454,1703,1572],{},[604,1705,1706],{"encoding":606},"-5",[568,1708,1710],{"className":1709,"ariaHidden":612},[611],[568,1711,1713,1716,1719],{"className":1712},[616],[568,1714],{"className":1715,"style":1662},[620],[568,1717,597],{"className":1718},[625],[568,1720,1572],{"className":1721},[625],[568,1723,1725,1738],{"className":1724},[571],[568,1726,1728],{"className":1727},[575],[577,1729,1730],{"xmlns":579},[581,1731,1732,1736],{},[584,1733,1734],{},[1454,1735,1572],{},[604,1737,1572],{"encoding":606},[568,1739,1741],{"className":1740,"ariaHidden":612},[611],[568,1742,1744,1747],{"className":1743},[616],[568,1745],{"className":1746,"style":1481},[620],[568,1748,1572],{"className":1749},[625]," liegen.",[568,1752,1754],{"className":1753},[986],[568,1755,1757,1829],{"className":1756},[571],[568,1758,1760],{"className":1759},[575],[577,1761,1762],{"xmlns":579,"display":995},[581,1763,1764,1826],{},[584,1765,1766,1768,1770,1772,1774,1776,1778,1780,1782,1784,1786,1789,1791,1793,1795,1797,1799,1801,1803,1806,1808,1810,1812,1814,1817,1819,1821,1823],{},[595,1767,597],{},[1454,1769,1572],{},[595,1771,743],{},[1454,1773,1558],{},[587,1775,593],{},[595,1777,597],{},[1454,1779,1565],{},[595,1781,743],{},[1454,1783,1572],{},[892,1785,1017],{},[595,1787,1788],{},"⇒",[892,1790,1017],{},[595,1792,597],{},[1454,1794,1558],{},[595,1796,743],{},[1454,1798,1558],{},[587,1800,593],{},[595,1802,743],{},[1454,1804,1805],{},"8",[892,1807,1017],{},[595,1809,1788],{},[892,1811,1017],{},[595,1813,597],{},[1454,1815,1816],{},"1",[595,1818,743],{},[587,1820,593],{},[595,1822,743],{},[1454,1824,1825],{},"4",[604,1827,1828],{"encoding":606},"-5 \\leq 2x - 3 \\leq 5 \\;\\Rightarrow\\; -2 \\leq 2x \\leq 8 \\;\\Rightarrow\\; -1 \\leq x \\leq 4",[568,1830,1832,1854,1875,1893,1917,1938,1959,1983,2004,2022],{"className":1831,"ariaHidden":612},[611],[568,1833,1835,1839,1842,1845,1848,1851],{"className":1834},[616],[568,1836],{"className":1837,"style":1838},[620],"height:0.7804em;vertical-align:-0.136em;",[568,1840,597],{"className":1841},[625],[568,1843,1572],{"className":1844},[625],[568,1846],{"className":1847,"style":789},[633],[568,1849,743],{"className":1850},[793],[568,1852],{"className":1853,"style":789},[633],[568,1855,1857,1860,1863,1866,1869,1872],{"className":1856},[616],[568,1858],{"className":1859,"style":1662},[620],[568,1861,1558],{"className":1862},[625],[568,1864,593],{"className":1865},[625,629],[568,1867],{"className":1868,"style":634},[633],[568,1870,597],{"className":1871},[638],[568,1873],{"className":1874,"style":634},[633],[568,1876,1878,1881,1884,1887,1890],{"className":1877},[616],[568,1879],{"className":1880,"style":1838},[620],[568,1882,1565],{"className":1883},[625],[568,1885],{"className":1886,"style":789},[633],[568,1888,743],{"className":1889},[793],[568,1891],{"className":1892,"style":789},[633],[568,1894,1896,1899,1902,1905,1908,1911,1914],{"className":1895},[616],[568,1897],{"className":1898,"style":1481},[620],[568,1900,1572],{"className":1901},[625],[568,1903],{"className":1904,"style":789},[633],[568,1906],{"className":1907,"style":789},[633],[568,1909,1788],{"className":1910},[793],[568,1912],{"className":1913,"style":789},[633],[568,1915],{"className":1916,"style":789},[633],[568,1918,1920,1923,1926,1929,1932,1935],{"className":1919},[616],[568,1921],{"className":1922,"style":1838},[620],[568,1924,597],{"className":1925},[625],[568,1927,1558],{"className":1928},[625],[568,1930],{"className":1931,"style":789},[633],[568,1933,743],{"className":1934},[793],[568,1936],{"className":1937,"style":789},[633],[568,1939,1941,1944,1947,1950,1953,1956],{"className":1940},[616],[568,1942],{"className":1943,"style":1838},[620],[568,1945,1558],{"className":1946},[625],[568,1948,593],{"className":1949},[625,629],[568,1951],{"className":1952,"style":789},[633],[568,1954,743],{"className":1955},[793],[568,1957],{"className":1958,"style":789},[633],[568,1960,1962,1965,1968,1971,1974,1977,1980],{"className":1961},[616],[568,1963],{"className":1964,"style":1481},[620],[568,1966,1805],{"className":1967},[625],[568,1969],{"className":1970,"style":789},[633],[568,1972],{"className":1973,"style":789},[633],[568,1975,1788],{"className":1976},[793],[568,1978],{"className":1979,"style":789},[633],[568,1981],{"className":1982,"style":789},[633],[568,1984,1986,1989,1992,1995,1998,2001],{"className":1985},[616],[568,1987],{"className":1988,"style":1838},[620],[568,1990,597],{"className":1991},[625],[568,1993,1816],{"className":1994},[625],[568,1996],{"className":1997,"style":789},[633],[568,1999,743],{"className":2000},[793],[568,2002],{"className":2003,"style":789},[633],[568,2005,2007,2010,2013,2016,2019],{"className":2006},[616],[568,2008],{"className":2009,"style":1279},[620],[568,2011,593],{"className":2012},[625,629],[568,2014],{"className":2015,"style":789},[633],[568,2017,743],{"className":2018},[793],[568,2020],{"className":2021,"style":789},[633],[568,2023,2025,2028],{"className":2024},[616],[568,2026],{"className":2027,"style":1481},[620],[568,2029,1825],{"className":2030},[625],[564,2032,2033,2034,689,2152,2251,2252,979],{},"Probe an den Rändern: ",[568,2035,2037,2077],{"className":2036},[571],[568,2038,2040],{"className":2039},[575],[577,2041,2042],{"xmlns":579},[581,2043,2044,2074],{},[584,2045,2046,2048,2050,2053,2056,2058,2060,2063,2065,2067,2069,2072],{},[587,2047,590],{"mathvariant":589},[1454,2049,1558],{},[595,2051,2052],{},"⋅",[595,2054,2055],{"stretchy":880},"(",[595,2057,597],{},[1454,2059,1816],{},[595,2061,2062],{"stretchy":880},")",[595,2064,597],{},[1454,2066,1565],{},[587,2068,590],{"mathvariant":589},[595,2070,2071],{},"=",[1454,2073,1572],{},[604,2075,2076],{"encoding":606},"|2 \\cdot (-1) - 3| = 5",[568,2078,2080,2098,2125,2143],{"className":2079,"ariaHidden":612},[611],[568,2081,2083,2086,2089,2092,2095],{"className":2082},[616],[568,2084],{"className":2085,"style":621},[620],[568,2087,1588],{"className":2088},[625],[568,2090],{"className":2091,"style":634},[633],[568,2093,2052],{"className":2094},[638],[568,2096],{"className":2097,"style":634},[633],[568,2099,2101,2104,2107,2110,2113,2116,2119,2122],{"className":2100},[616],[568,2102],{"className":2103,"style":621},[620],[568,2105,2055],{"className":2106},[920],[568,2108,597],{"className":2109},[625],[568,2111,1816],{"className":2112},[625],[568,2114,2062],{"className":2115},[978],[568,2117],{"className":2118,"style":634},[633],[568,2120,597],{"className":2121},[638],[568,2123],{"className":2124,"style":634},[633],[568,2126,2128,2131,2134,2137,2140],{"className":2127},[616],[568,2129],{"className":2130,"style":621},[620],[568,2132,1610],{"className":2133},[625],[568,2135],{"className":2136,"style":789},[633],[568,2138,2071],{"className":2139},[793],[568,2141],{"className":2142,"style":789},[633],[568,2144,2146,2149],{"className":2145},[616],[568,2147],{"className":2148,"style":1481},[620],[568,2150,1572],{"className":2151},[625],[568,2153,2155,2185],{"className":2154},[571],[568,2156,2158],{"className":2157},[575],[577,2159,2160],{"xmlns":579},[581,2161,2162,2182],{},[584,2163,2164,2166,2168,2170,2172,2174,2176,2178,2180],{},[587,2165,590],{"mathvariant":589},[1454,2167,1558],{},[595,2169,2052],{},[1454,2171,1825],{},[595,2173,597],{},[1454,2175,1565],{},[587,2177,590],{"mathvariant":589},[595,2179,2071],{},[1454,2181,1572],{},[604,2183,2184],{"encoding":606},"|2 \\cdot 4 - 3| = 5",[568,2186,2188,2206,2224,2242],{"className":2187,"ariaHidden":612},[611],[568,2189,2191,2194,2197,2200,2203],{"className":2190},[616],[568,2192],{"className":2193,"style":621},[620],[568,2195,1588],{"className":2196},[625],[568,2198],{"className":2199,"style":634},[633],[568,2201,2052],{"className":2202},[638],[568,2204],{"className":2205,"style":634},[633],[568,2207,2209,2212,2215,2218,2221],{"className":2208},[616],[568,2210],{"className":2211,"style":1662},[620],[568,2213,1825],{"className":2214},[625],[568,2216],{"className":2217,"style":634},[633],[568,2219,597],{"className":2220},[638],[568,2222],{"className":2223,"style":634},[633],[568,2225,2227,2230,2233,2236,2239],{"className":2226},[616],[568,2228],{"className":2229,"style":621},[620],[568,2231,1610],{"className":2232},[625],[568,2234],{"className":2235,"style":789},[633],[568,2237,2071],{"className":2238},[793],[568,2240],{"className":2241,"style":789},[633],[568,2243,2245,2248],{"className":2244},[616],[568,2246],{"className":2247,"style":1481},[620],[568,2249,1572],{"className":2250},[625],". Lösungsmenge ",[568,2253,2255,2287],{"className":2254},[571],[568,2256,2258],{"className":2257},[575],[577,2259,2260],{"xmlns":579},[581,2261,2262,2284],{},[584,2263,2264,2268,2270,2272,2274,2276,2278,2280,2282],{},[587,2265,2267],{"mathvariant":2266},"double-struck","L",[595,2269,2071],{},[595,2271,881],{"stretchy":880},[595,2273,597],{},[1454,2275,1816],{},[595,2277,890],{"separator":612},[892,2279,894],{},[1454,2281,1825],{},[595,2283,904],{"stretchy":880},[604,2285,2286],{"encoding":606},"\\mathbb{L} = [-1;\\ 4]",[568,2288,2290,2310],{"className":2289,"ariaHidden":612},[611],[568,2291,2293,2297,2301,2304,2307],{"className":2292},[616],[568,2294],{"className":2295,"style":2296},[620],"height:0.6889em;",[568,2298,2267],{"className":2299},[625,2300],"mathbb",[568,2302],{"className":2303,"style":789},[633],[568,2305,2071],{"className":2306},[793],[568,2308],{"className":2309,"style":789},[633],[568,2311,2313,2316,2319,2322,2325,2328,2331,2334,2337],{"className":2312},[616],[568,2314],{"className":2315,"style":621},[620],[568,2317,881],{"className":2318},[920],[568,2320,597],{"className":2321},[625],[568,2323,1816],{"className":2324},[625],[568,2326,890],{"className":2327},[946],[568,2329,894],{"className":2330},[633],[568,2332],{"className":2333,"style":953},[633],[568,2335,1825],{"className":2336},[625],[568,2338,904],{"className":2339},[978],[564,2341,2342,2423,2424,689,2480,2531,2532,979],{},[568,2343,2345,2371],{"className":2344},[571],[568,2346,2348],{"className":2347},[575],[577,2349,2350],{"xmlns":579},[581,2351,2352,2368],{},[584,2353,2354,2356,2358,2360,2362,2364,2366],{},[587,2355,590],{"mathvariant":589},[587,2357,593],{},[595,2359,899],{},[1454,2361,1816],{},[587,2363,590],{"mathvariant":589},[595,2365,1012],{},[1454,2367,1565],{},[604,2369,2370],{"encoding":606},"|x + 1| > 3",[568,2372,2374,2395,2414],{"className":2373,"ariaHidden":612},[611],[568,2375,2377,2380,2383,2386,2389,2392],{"className":2376},[616],[568,2378],{"className":2379,"style":621},[620],[568,2381,590],{"className":2382},[625],[568,2384,593],{"className":2385},[625,629],[568,2387],{"className":2388,"style":634},[633],[568,2390,899],{"className":2391},[638],[568,2393],{"className":2394,"style":634},[633],[568,2396,2398,2401,2405,2408,2411],{"className":2397},[616],[568,2399],{"className":2400,"style":621},[620],[568,2402,2404],{"className":2403},[625],"1∣",[568,2406],{"className":2407,"style":789},[633],[568,2409,1012],{"className":2410},[793],[568,2412],{"className":2413,"style":789},[633],[568,2415,2417,2420],{"className":2416},[616],[568,2418],{"className":2419,"style":1481},[620],[568,2421,1565],{"className":2422},[625],": Hier ist ",[568,2425,2427,2447],{"className":2426},[571],[568,2428,2430],{"className":2429},[575],[577,2431,2432],{"xmlns":579},[581,2433,2434,2444],{},[584,2435,2436,2438,2440,2442],{},[587,2437,600],{},[595,2439,2071],{},[595,2441,597],{},[1454,2443,1816],{},[604,2445,2446],{"encoding":606},"a = -1",[568,2448,2450,2468],{"className":2449,"ariaHidden":612},[611],[568,2451,2453,2456,2459,2462,2465],{"className":2452},[616],[568,2454],{"className":2455,"style":685},[620],[568,2457,600],{"className":2458},[625,629],[568,2460],{"className":2461,"style":789},[633],[568,2463,2071],{"className":2464},[793],[568,2466],{"className":2467,"style":789},[633],[568,2469,2471,2474,2477],{"className":2470},[616],[568,2472],{"className":2473,"style":1662},[620],[568,2475,597],{"className":2476},[625],[568,2478,1816],{"className":2479},[625],[568,2481,2483,2501],{"className":2482},[571],[568,2484,2486],{"className":2485},[575],[577,2487,2488],{"xmlns":579},[581,2489,2490,2498],{},[584,2491,2492,2494,2496],{},[587,2493,746],{},[595,2495,2071],{},[1454,2497,1565],{},[604,2499,2500],{"encoding":606},"r = 3",[568,2502,2504,2522],{"className":2503,"ariaHidden":612},[611],[568,2505,2507,2510,2513,2516,2519],{"className":2506},[616],[568,2508],{"className":2509,"style":685},[620],[568,2511,746],{"className":2512,"style":806},[625,629],[568,2514],{"className":2515,"style":789},[633],[568,2517,2071],{"className":2518},[793],[568,2520],{"className":2521,"style":789},[633],[568,2523,2525,2528],{"className":2524},[616],[568,2526],{"className":2527,"style":1481},[620],[568,2529,1565],{"className":2530},[625],", denn ",[568,2533,2535,2567],{"className":2534},[571],[568,2536,2538],{"className":2537},[575],[577,2539,2540],{"xmlns":579},[581,2541,2542,2564],{},[584,2543,2544,2546,2548,2550,2552,2554,2556,2558,2560,2562],{},[587,2545,593],{},[595,2547,899],{},[1454,2549,1816],{},[595,2551,2071],{},[587,2553,593],{},[595,2555,597],{},[595,2557,2055],{"stretchy":880},[595,2559,597],{},[1454,2561,1816],{},[595,2563,2062],{"stretchy":880},[604,2565,2566],{"encoding":606},"x + 1 = x - (-1)",[568,2568,2570,2588,2606,2624],{"className":2569,"ariaHidden":612},[611],[568,2571,2573,2576,2579,2582,2585],{"className":2572},[616],[568,2574],{"className":2575,"style":1145},[620],[568,2577,593],{"className":2578},[625,629],[568,2580],{"className":2581,"style":634},[633],[568,2583,899],{"className":2584},[638],[568,2586],{"className":2587,"style":634},[633],[568,2589,2591,2594,2597,2600,2603],{"className":2590},[616],[568,2592],{"className":2593,"style":1481},[620],[568,2595,1816],{"className":2596},[625],[568,2598],{"className":2599,"style":789},[633],[568,2601,2071],{"className":2602},[793],[568,2604],{"className":2605,"style":789},[633],[568,2607,2609,2612,2615,2618,2621],{"className":2608},[616],[568,2610],{"className":2611,"style":1145},[620],[568,2613,593],{"className":2614},[625,629],[568,2616],{"className":2617,"style":634},[633],[568,2619,597],{"className":2620},[638],[568,2622],{"className":2623,"style":634},[633],[568,2625,2627,2630,2633,2636,2639],{"className":2626},[616],[568,2628],{"className":2629,"style":621},[620],[568,2631,2055],{"className":2632},[920],[568,2634,597],{"className":2635},[625],[568,2637,1816],{"className":2638},[625],[568,2640,2062],{"className":2641},[978],[568,2643,2645],{"className":2644},[986],[568,2646,2648,2702],{"className":2647},[571],[568,2649,2651],{"className":2650},[575],[577,2652,2653],{"xmlns":579,"display":995},[581,2654,2655,2699],{},[584,2656,2657,2659,2661,2663,2665,2667,2669,2671,2673,2675,2678,2681,2683,2685,2687,2689,2691,2693,2695,2697],{},[587,2658,593],{},[595,2660,1027],{},[595,2662,597],{},[1454,2664,1816],{},[595,2666,597],{},[1454,2668,1565],{},[595,2670,2071],{},[595,2672,597],{},[1454,2674,1825],{},[633,2676],{"width":2677},"1em",[892,2679,2680],{},"oder",[633,2682],{"width":2677},[587,2684,593],{},[595,2686,1012],{},[595,2688,597],{},[1454,2690,1816],{},[595,2692,899],{},[1454,2694,1565],{},[595,2696,2071],{},[1454,2698,1558],{},[604,2700,2701],{"encoding":606},"x \u003C -1 - 3 = -4 \\quad \\text{oder} \\quad x > -1 + 3 = 2",[568,2703,2705,2723,2744,2762,2800,2821,2839],{"className":2704,"ariaHidden":612},[611],[568,2706,2708,2711,2714,2717,2720],{"className":2707},[616],[568,2709],{"className":2710,"style":1126},[620],[568,2712,593],{"className":2713},[625,629],[568,2715],{"className":2716,"style":789},[633],[568,2718,1027],{"className":2719},[793],[568,2721],{"className":2722,"style":789},[633],[568,2724,2726,2729,2732,2735,2738,2741],{"className":2725},[616],[568,2727],{"className":2728,"style":1662},[620],[568,2730,597],{"className":2731},[625],[568,2733,1816],{"className":2734},[625],[568,2736],{"className":2737,"style":634},[633],[568,2739,597],{"className":2740},[638],[568,2742],{"className":2743,"style":634},[633],[568,2745,2747,2750,2753,2756,2759],{"className":2746},[616],[568,2748],{"className":2749,"style":1481},[620],[568,2751,1565],{"className":2752},[625],[568,2754],{"className":2755,"style":789},[633],[568,2757,2071],{"className":2758},[793],[568,2760],{"className":2761,"style":789},[633],[568,2763,2765,2769,2772,2775,2779,2785,2788,2791,2794,2797],{"className":2764},[616],[568,2766],{"className":2767,"style":2768},[620],"height:0.7778em;vertical-align:-0.0833em;",[568,2770,597],{"className":2771},[625],[568,2773,1825],{"className":2774},[625],[568,2776],{"className":2777,"style":2778},[633],"margin-right:1em;",[568,2780,2782],{"className":2781},[625,1174],[568,2783,2680],{"className":2784},[625],[568,2786],{"className":2787,"style":2778},[633],[568,2789,593],{"className":2790},[625,629],[568,2792],{"className":2793,"style":789},[633],[568,2795,1012],{"className":2796},[793],[568,2798],{"className":2799,"style":789},[633],[568,2801,2803,2806,2809,2812,2815,2818],{"className":2802},[616],[568,2804],{"className":2805,"style":1662},[620],[568,2807,597],{"className":2808},[625],[568,2810,1816],{"className":2811},[625],[568,2813],{"className":2814,"style":634},[633],[568,2816,899],{"className":2817},[638],[568,2819],{"className":2820,"style":634},[633],[568,2822,2824,2827,2830,2833,2836],{"className":2823},[616],[568,2825],{"className":2826,"style":1481},[620],[568,2828,1565],{"className":2829},[625],[568,2831],{"className":2832,"style":789},[633],[568,2834,2071],{"className":2835},[793],[568,2837],{"className":2838,"style":789},[633],[568,2840,2842,2845],{"className":2841},[616],[568,2843],{"className":2844,"style":1481},[620],[568,2846,1558],{"className":2847},[625],[564,2849,2850,2851,979],{},"Lösungsmenge ",[568,2852,2854,2896],{"className":2853},[571],[568,2855,2857],{"className":2856},[575],[577,2858,2859],{"xmlns":579},[581,2860,2861,2893],{},[584,2862,2863,2865,2867,2870,2872,2874,2876,2878,2880,2882,2884,2886,2888,2890],{},[587,2864,2267],{"mathvariant":2266},[595,2866,2071],{},[595,2868,2869],{"stretchy":880},"{",[587,2871,593],{},[595,2873,590],{},[587,2875,593],{},[595,2877,1027],{},[595,2879,597],{},[1454,2881,1825],{},[892,2883,1178],{},[587,2885,593],{},[595,2887,1012],{},[1454,2889,1558],{},[595,2891,2892],{"stretchy":880},"}",[604,2894,2895],{"encoding":606},"\\mathbb{L} = \\{x \\mid x \u003C -4 \\text{ oder } x > 2\\}",[568,2897,2899,2917,2938,2956,2986],{"className":2898,"ariaHidden":612},[611],[568,2900,2902,2905,2908,2911,2914],{"className":2901},[616],[568,2903],{"className":2904,"style":2296},[620],[568,2906,2267],{"className":2907},[625,2300],[568,2909],{"className":2910,"style":789},[633],[568,2912,2071],{"className":2913},[793],[568,2915],{"className":2916,"style":789},[633],[568,2918,2920,2923,2926,2929,2932,2935],{"className":2919},[616],[568,2921],{"className":2922,"style":621},[620],[568,2924,2869],{"className":2925},[920],[568,2927,593],{"className":2928},[625,629],[568,2930],{"className":2931,"style":789},[633],[568,2933,590],{"className":2934},[793],[568,2936],{"className":2937,"style":789},[633],[568,2939,2941,2944,2947,2950,2953],{"className":2940},[616],[568,2942],{"className":2943,"style":1126},[620],[568,2945,593],{"className":2946},[625,629],[568,2948],{"className":2949,"style":789},[633],[568,2951,1027],{"className":2952},[793],[568,2954],{"className":2955,"style":789},[633],[568,2957,2959,2962,2965,2968,2974,2977,2980,2983],{"className":2958},[616],[568,2960],{"className":2961,"style":2768},[620],[568,2963,597],{"className":2964},[625],[568,2966,1825],{"className":2967},[625],[568,2969,2971],{"className":2970},[625,1174],[568,2972,1178],{"className":2973},[625],[568,2975,593],{"className":2976},[625,629],[568,2978],{"className":2979,"style":789},[633],[568,2981,1012],{"className":2982},[793],[568,2984],{"className":2985,"style":789},[633],[568,2987,2989,2992,2995],{"className":2988},[616],[568,2990],{"className":2991,"style":621},[620],[568,2993,1558],{"className":2994},[625],[568,2996,2892],{"className":2997},[978],[564,2999,3000,3001,979],{},"Mit Fallunterscheidung: ",[568,3002,3004,3036],{"className":3003},[571],[568,3005,3007],{"className":3006},[575],[577,3008,3009],{"xmlns":579},[581,3010,3011,3033],{},[584,3012,3013,3015,3017,3019,3021,3023,3025,3027,3029,3031],{},[587,3014,590],{"mathvariant":589},[587,3016,593],{},[595,3018,597],{},[1454,3020,1558],{},[587,3022,590],{"mathvariant":589},[595,3024,1027],{},[1454,3026,1558],{},[587,3028,593],{},[595,3030,899],{},[1454,3032,1816],{},[604,3034,3035],{"encoding":606},"|x - 2| \u003C 2x + 1",[568,3037,3039,3060,3079,3100],{"className":3038,"ariaHidden":612},[611],[568,3040,3042,3045,3048,3051,3054,3057],{"className":3041},[616],[568,3043],{"className":3044,"style":621},[620],[568,3046,590],{"className":3047},[625],[568,3049,593],{"className":3050},[625,629],[568,3052],{"className":3053,"style":634},[633],[568,3055,597],{"className":3056},[638],[568,3058],{"className":3059,"style":634},[633],[568,3061,3063,3066,3070,3073,3076],{"className":3062},[616],[568,3064],{"className":3065,"style":621},[620],[568,3067,3069],{"className":3068},[625],"2∣",[568,3071],{"className":3072,"style":789},[633],[568,3074,1027],{"className":3075},[793],[568,3077],{"className":3078,"style":789},[633],[568,3080,3082,3085,3088,3091,3094,3097],{"className":3081},[616],[568,3083],{"className":3084,"style":1662},[620],[568,3086,1558],{"className":3087},[625],[568,3089,593],{"className":3090},[625,629],[568,3092],{"className":3093,"style":634},[633],[568,3095,899],{"className":3096},[638],[568,3098],{"className":3099,"style":634},[633],[568,3101,3103,3106],{"className":3102},[616],[568,3104],{"className":3105,"style":1481},[620],[568,3107,1816],{"className":3108},[625],[1433,3110,3111,3426],{},[1436,3112,3113,3114,3165,3166,3267,3268,3324,3325,3375,3376,979],{},"Fall ",[568,3115,3117,3135],{"className":3116},[571],[568,3118,3120],{"className":3119},[575],[577,3121,3122],{"xmlns":579},[581,3123,3124,3132],{},[584,3125,3126,3128,3130],{},[587,3127,593],{},[595,3129,1266],{},[1454,3131,1558],{},[604,3133,3134],{"encoding":606},"x \\geq 2",[568,3136,3138,3156],{"className":3137,"ariaHidden":612},[611],[568,3139,3141,3144,3147,3150,3153],{"className":3140},[616],[568,3142],{"className":3143,"style":1279},[620],[568,3145,593],{"className":3146},[625,629],[568,3148],{"className":3149,"style":789},[633],[568,3151,1266],{"className":3152},[793],[568,3154],{"className":3155,"style":789},[633],[568,3157,3159,3162],{"className":3158},[616],[568,3160],{"className":3161,"style":1481},[620],[568,3163,1558],{"className":3164},[625],": ",[568,3167,3169,3197],{"className":3168},[571],[568,3170,3172],{"className":3171},[575],[577,3173,3174],{"xmlns":579},[581,3175,3176,3194],{},[584,3177,3178,3180,3182,3184,3186,3188,3190,3192],{},[587,3179,593],{},[595,3181,597],{},[1454,3183,1558],{},[595,3185,1027],{},[1454,3187,1558],{},[587,3189,593],{},[595,3191,899],{},[1454,3193,1816],{},[604,3195,3196],{"encoding":606},"x - 2 \u003C 2x + 1",[568,3198,3200,3218,3237,3258],{"className":3199,"ariaHidden":612},[611],[568,3201,3203,3206,3209,3212,3215],{"className":3202},[616],[568,3204],{"className":3205,"style":1145},[620],[568,3207,593],{"className":3208},[625,629],[568,3210],{"className":3211,"style":634},[633],[568,3213,597],{"className":3214},[638],[568,3216],{"className":3217,"style":634},[633],[568,3219,3221,3225,3228,3231,3234],{"className":3220},[616],[568,3222],{"className":3223,"style":3224},[620],"height:0.6835em;vertical-align:-0.0391em;",[568,3226,1558],{"className":3227},[625],[568,3229],{"className":3230,"style":789},[633],[568,3232,1027],{"className":3233},[793],[568,3235],{"className":3236,"style":789},[633],[568,3238,3240,3243,3246,3249,3252,3255],{"className":3239},[616],[568,3241],{"className":3242,"style":1662},[620],[568,3244,1558],{"className":3245},[625],[568,3247,593],{"className":3248},[625,629],[568,3250],{"className":3251,"style":634},[633],[568,3253,899],{"className":3254},[638],[568,3256],{"className":3257,"style":634},[633],[568,3259,3261,3264],{"className":3260},[616],[568,3262],{"className":3263,"style":1481},[620],[568,3265,1816],{"className":3266},[625],", also ",[568,3269,3271,3291],{"className":3270},[571],[568,3272,3274],{"className":3273},[575],[577,3275,3276],{"xmlns":579},[581,3277,3278,3288],{},[584,3279,3280,3282,3284,3286],{},[587,3281,593],{},[595,3283,1012],{},[595,3285,597],{},[1454,3287,1565],{},[604,3289,3290],{"encoding":606},"x > -3",[568,3292,3294,3312],{"className":3293,"ariaHidden":612},[611],[568,3295,3297,3300,3303,3306,3309],{"className":3296},[616],[568,3298],{"className":3299,"style":1126},[620],[568,3301,593],{"className":3302},[625,629],[568,3304],{"className":3305,"style":789},[633],[568,3307,1012],{"className":3308},[793],[568,3310],{"className":3311,"style":789},[633],[568,3313,3315,3318,3321],{"className":3314},[616],[568,3316],{"className":3317,"style":1662},[620],[568,3319,597],{"className":3320},[625],[568,3322,1565],{"className":3323},[625],". Zusammen mit ",[568,3326,3328,3345],{"className":3327},[571],[568,3329,3331],{"className":3330},[575],[577,3332,3333],{"xmlns":579},[581,3334,3335,3343],{},[584,3336,3337,3339,3341],{},[587,3338,593],{},[595,3340,1266],{},[1454,3342,1558],{},[604,3344,3134],{"encoding":606},[568,3346,3348,3366],{"className":3347,"ariaHidden":612},[611],[568,3349,3351,3354,3357,3360,3363],{"className":3350},[616],[568,3352],{"className":3353,"style":1279},[620],[568,3355,593],{"className":3356},[625,629],[568,3358],{"className":3359,"style":789},[633],[568,3361,1266],{"className":3362},[793],[568,3364],{"className":3365,"style":789},[633],[568,3367,3369,3372],{"className":3368},[616],[568,3370],{"className":3371,"style":1481},[620],[568,3373,1558],{"className":3374},[625]," gilt das für alle ",[568,3377,3379,3396],{"className":3378},[571],[568,3380,3382],{"className":3381},[575],[577,3383,3384],{"xmlns":579},[581,3385,3386,3394],{},[584,3387,3388,3390,3392],{},[587,3389,593],{},[595,3391,1266],{},[1454,3393,1558],{},[604,3395,3134],{"encoding":606},[568,3397,3399,3417],{"className":3398,"ariaHidden":612},[611],[568,3400,3402,3405,3408,3411,3414],{"className":3401},[616],[568,3403],{"className":3404,"style":1279},[620],[568,3406,593],{"className":3407},[625,629],[568,3409],{"className":3410,"style":789},[633],[568,3412,1266],{"className":3413},[793],[568,3415],{"className":3416,"style":789},[633],[568,3418,3420,3423],{"className":3419},[616],[568,3421],{"className":3422,"style":1481},[620],[568,3424,1558],{"className":3425},[625],[1436,3427,3113,3428,3165,3479,3267,3594,3694,3695,3837,3838,979],{},[568,3429,3431,3449],{"className":3430},[571],[568,3432,3434],{"className":3433},[575],[577,3435,3436],{"xmlns":579},[581,3437,3438,3446],{},[584,3439,3440,3442,3444],{},[587,3441,593],{},[595,3443,1027],{},[1454,3445,1558],{},[604,3447,3448],{"encoding":606},"x \u003C 2",[568,3450,3452,3470],{"className":3451,"ariaHidden":612},[611],[568,3453,3455,3458,3461,3464,3467],{"className":3454},[616],[568,3456],{"className":3457,"style":1126},[620],[568,3459,593],{"className":3460},[625,629],[568,3462],{"className":3463,"style":789},[633],[568,3465,1027],{"className":3466},[793],[568,3468],{"className":3469,"style":789},[633],[568,3471,3473,3476],{"className":3472},[616],[568,3474],{"className":3475,"style":1481},[620],[568,3477,1558],{"className":3478},[625],[568,3480,3482,3516],{"className":3481},[571],[568,3483,3485],{"className":3484},[575],[577,3486,3487],{"xmlns":579},[581,3488,3489,3513],{},[584,3490,3491,3493,3495,3497,3499,3501,3503,3505,3507,3509,3511],{},[595,3492,597],{},[595,3494,2055],{"stretchy":880},[587,3496,593],{},[595,3498,597],{},[1454,3500,1558],{},[595,3502,2062],{"stretchy":880},[595,3504,1027],{},[1454,3506,1558],{},[587,3508,593],{},[595,3510,899],{},[1454,3512,1816],{},[604,3514,3515],{"encoding":606},"-(x - 2) \u003C 2x + 1",[568,3517,3519,3543,3564,3585],{"className":3518,"ariaHidden":612},[611],[568,3520,3522,3525,3528,3531,3534,3537,3540],{"className":3521},[616],[568,3523],{"className":3524,"style":621},[620],[568,3526,597],{"className":3527},[625],[568,3529,2055],{"className":3530},[920],[568,3532,593],{"className":3533},[625,629],[568,3535],{"className":3536,"style":634},[633],[568,3538,597],{"className":3539},[638],[568,3541],{"className":3542,"style":634},[633],[568,3544,3546,3549,3552,3555,3558,3561],{"className":3545},[616],[568,3547],{"className":3548,"style":621},[620],[568,3550,1558],{"className":3551},[625],[568,3553,2062],{"className":3554},[978],[568,3556],{"className":3557,"style":789},[633],[568,3559,1027],{"className":3560},[793],[568,3562],{"className":3563,"style":789},[633],[568,3565,3567,3570,3573,3576,3579,3582],{"className":3566},[616],[568,3568],{"className":3569,"style":1662},[620],[568,3571,1558],{"className":3572},[625],[568,3574,593],{"className":3575},[625,629],[568,3577],{"className":3578,"style":634},[633],[568,3580,899],{"className":3581},[638],[568,3583],{"className":3584,"style":634},[633],[568,3586,3588,3591],{"className":3587},[616],[568,3589],{"className":3590,"style":1481},[620],[568,3592,1816],{"className":3593},[625],[568,3595,3597,3625],{"className":3596},[571],[568,3598,3600],{"className":3599},[575],[577,3601,3602],{"xmlns":579},[581,3603,3604,3622],{},[584,3605,3606,3608,3610,3612,3614,3616,3618,3620],{},[1454,3607,1558],{},[595,3609,597],{},[587,3611,593],{},[595,3613,1027],{},[1454,3615,1558],{},[587,3617,593],{},[595,3619,899],{},[1454,3621,1816],{},[604,3623,3624],{"encoding":606},"2 - x \u003C 2x + 1",[568,3626,3628,3646,3664,3685],{"className":3627,"ariaHidden":612},[611],[568,3629,3631,3634,3637,3640,3643],{"className":3630},[616],[568,3632],{"className":3633,"style":1662},[620],[568,3635,1558],{"className":3636},[625],[568,3638],{"className":3639,"style":634},[633],[568,3641,597],{"className":3642},[638],[568,3644],{"className":3645,"style":634},[633],[568,3647,3649,3652,3655,3658,3661],{"className":3648},[616],[568,3650],{"className":3651,"style":1126},[620],[568,3653,593],{"className":3654},[625,629],[568,3656],{"className":3657,"style":789},[633],[568,3659,1027],{"className":3660},[793],[568,3662],{"className":3663,"style":789},[633],[568,3665,3667,3670,3673,3676,3679,3682],{"className":3666},[616],[568,3668],{"className":3669,"style":1662},[620],[568,3671,1558],{"className":3672},[625],[568,3674,593],{"className":3675},[625,629],[568,3677],{"className":3678,"style":634},[633],[568,3680,899],{"className":3681},[638],[568,3683],{"className":3684,"style":634},[633],[568,3686,3688,3691],{"className":3687},[616],[568,3689],{"className":3690,"style":1481},[620],[568,3692,1816],{"className":3693},[625]," und damit ",[568,3696,3698,3721],{"className":3697},[571],[568,3699,3701],{"className":3700},[575],[577,3702,3703],{"xmlns":579},[581,3704,3705,3718],{},[584,3706,3707,3709,3711],{},[587,3708,593],{},[595,3710,1012],{},[3712,3713,3714,3716],"mfrac",{},[1454,3715,1816],{},[1454,3717,1565],{},[604,3719,3720],{"encoding":606},"x > \\frac{1}{3}",[568,3722,3724,3742],{"className":3723,"ariaHidden":612},[611],[568,3725,3727,3730,3733,3736,3739],{"className":3726},[616],[568,3728],{"className":3729,"style":1126},[620],[568,3731,593],{"className":3732},[625,629],[568,3734],{"className":3735,"style":789},[633],[568,3737,1012],{"className":3738},[793],[568,3740],{"className":3741,"style":789},[633],[568,3743,3745,3749],{"className":3744},[616],[568,3746],{"className":3747,"style":3748},[620],"height:1.1901em;vertical-align:-0.345em;",[568,3750,3752,3756,3834],{"className":3751},[625],[568,3753],{"className":3754},[920,3755],"nulldelimiter",[568,3757,3759],{"className":3758},[3712],[568,3760,3764,3825],{"className":3761},[3762,3763],"vlist-t","vlist-t2",[568,3765,3768,3820],{"className":3766},[3767],"vlist-r",[568,3769,3773,3794,3805],{"className":3770,"style":3772},[3771],"vlist","height:0.8451em;",[568,3774,3776,3781],{"style":3775},"top:-2.655em;",[568,3777],{"className":3778,"style":3780},[3779],"pstrut","height:3em;",[568,3782,3788],{"className":3783},[3784,3785,3786,3787],"sizing","reset-size6","size3","mtight",[568,3789,3791],{"className":3790},[625,3787],[568,3792,1565],{"className":3793},[625,3787],[568,3795,3797,3800],{"style":3796},"top:-3.23em;",[568,3798],{"className":3799,"style":3780},[3779],[568,3801],{"className":3802,"style":3804},[3803],"frac-line","border-bottom-width:0.04em;",[568,3806,3808,3811],{"style":3807},"top:-3.394em;",[568,3809],{"className":3810,"style":3780},[3779],[568,3812,3814],{"className":3813},[3784,3785,3786,3787],[568,3815,3817],{"className":3816},[625,3787],[568,3818,1816],{"className":3819},[625,3787],[568,3821,3824],{"className":3822},[3823],"vlist-s","​",[568,3826,3828],{"className":3827},[3767],[568,3829,3832],{"className":3830,"style":3831},[3771],"height:0.345em;",[568,3833],{},[568,3835],{"className":3836},[978,3755],". Zusammen: ",[568,3839,3841,3867],{"className":3840},[571],[568,3842,3844],{"className":3843},[575],[577,3845,3846],{"xmlns":579},[581,3847,3848,3864],{},[584,3849,3850,3856,3858,3860,3862],{},[3712,3851,3852,3854],{},[1454,3853,1816],{},[1454,3855,1565],{},[595,3857,1027],{},[587,3859,593],{},[595,3861,1027],{},[1454,3863,1558],{},[604,3865,3866],{"encoding":606},"\\frac{1}{3} \u003C x \u003C 2",[568,3868,3870,3953,3971],{"className":3869,"ariaHidden":612},[611],[568,3871,3873,3876,3944,3947,3950],{"className":3872},[616],[568,3874],{"className":3875,"style":3748},[620],[568,3877,3879,3882,3941],{"className":3878},[625],[568,3880],{"className":3881},[920,3755],[568,3883,3885],{"className":3884},[3712],[568,3886,3888,3933],{"className":3887},[3762,3763],[568,3889,3891,3930],{"className":3890},[3767],[568,3892,3894,3908,3916],{"className":3893,"style":3772},[3771],[568,3895,3896,3899],{"style":3775},[568,3897],{"className":3898,"style":3780},[3779],[568,3900,3902],{"className":3901},[3784,3785,3786,3787],[568,3903,3905],{"className":3904},[625,3787],[568,3906,1565],{"className":3907},[625,3787],[568,3909,3910,3913],{"style":3796},[568,3911],{"className":3912,"style":3780},[3779],[568,3914],{"className":3915,"style":3804},[3803],[568,3917,3918,3921],{"style":3807},[568,3919],{"className":3920,"style":3780},[3779],[568,3922,3924],{"className":3923},[3784,3785,3786,3787],[568,3925,3927],{"className":3926},[625,3787],[568,3928,1816],{"className":3929},[625,3787],[568,3931,3824],{"className":3932},[3823],[568,3934,3936],{"className":3935},[3767],[568,3937,3939],{"className":3938,"style":3831},[3771],[568,3940],{},[568,3942],{"className":3943},[978,3755],[568,3945],{"className":3946,"style":789},[633],[568,3948,1027],{"className":3949},[793],[568,3951],{"className":3952,"style":789},[633],[568,3954,3956,3959,3962,3965,3968],{"className":3955},[616],[568,3957],{"className":3958,"style":1126},[620],[568,3960,593],{"className":3961},[625,629],[568,3963],{"className":3964,"style":789},[633],[568,3966,1027],{"className":3967},[793],[568,3969],{"className":3970,"style":789},[633],[568,3972,3974,3977],{"className":3973},[616],[568,3975],{"className":3976,"style":1481},[620],[568,3978,1558],{"className":3979},[625],[564,3981,3982,3983,4157,4158,3165,4209,4310,4311,3165,4362,4440,4441,4536],{},"Vereinigt: ",[568,3984,3986,4020],{"className":3985},[571],[568,3987,3989],{"className":3988},[575],[577,3990,3991],{"xmlns":579},[581,3992,3993,4017],{},[584,3994,3995,3997,3999,4001,4003,4005,4007,4009,4015],{},[587,3996,2267],{"mathvariant":2266},[595,3998,2071],{},[595,4000,2869],{"stretchy":880},[587,4002,593],{},[595,4004,590],{},[587,4006,593],{},[595,4008,1012],{},[3712,4010,4011,4013],{},[1454,4012,1816],{},[1454,4014,1565],{},[595,4016,2892],{"stretchy":880},[604,4018,4019],{"encoding":606},"\\mathbb{L} = \\{x \\mid x > \\frac{1}{3}\\}",[568,4021,4023,4041,4062,4080],{"className":4022,"ariaHidden":612},[611],[568,4024,4026,4029,4032,4035,4038],{"className":4025},[616],[568,4027],{"className":4028,"style":2296},[620],[568,4030,2267],{"className":4031},[625,2300],[568,4033],{"className":4034,"style":789},[633],[568,4036,2071],{"className":4037},[793],[568,4039],{"className":4040,"style":789},[633],[568,4042,4044,4047,4050,4053,4056,4059],{"className":4043},[616],[568,4045],{"className":4046,"style":621},[620],[568,4048,2869],{"className":4049},[920],[568,4051,593],{"className":4052},[625,629],[568,4054],{"className":4055,"style":789},[633],[568,4057,590],{"className":4058},[793],[568,4060],{"className":4061,"style":789},[633],[568,4063,4065,4068,4071,4074,4077],{"className":4064},[616],[568,4066],{"className":4067,"style":1126},[620],[568,4069,593],{"className":4070},[625,629],[568,4072],{"className":4073,"style":789},[633],[568,4075,1012],{"className":4076},[793],[568,4078],{"className":4079,"style":789},[633],[568,4081,4083,4086,4154],{"className":4082},[616],[568,4084],{"className":4085,"style":3748},[620],[568,4087,4089,4092,4151],{"className":4088},[625],[568,4090],{"className":4091},[920,3755],[568,4093,4095],{"className":4094},[3712],[568,4096,4098,4143],{"className":4097},[3762,3763],[568,4099,4101,4140],{"className":4100},[3767],[568,4102,4104,4118,4126],{"className":4103,"style":3772},[3771],[568,4105,4106,4109],{"style":3775},[568,4107],{"className":4108,"style":3780},[3779],[568,4110,4112],{"className":4111},[3784,3785,3786,3787],[568,4113,4115],{"className":4114},[625,3787],[568,4116,1565],{"className":4117},[625,3787],[568,4119,4120,4123],{"style":3796},[568,4121],{"className":4122,"style":3780},[3779],[568,4124],{"className":4125,"style":3804},[3803],[568,4127,4128,4131],{"style":3807},[568,4129],{"className":4130,"style":3780},[3779],[568,4132,4134],{"className":4133},[3784,3785,3786,3787],[568,4135,4137],{"className":4136},[625,3787],[568,4138,1816],{"className":4139},[625,3787],[568,4141,3824],{"className":4142},[3823],[568,4144,4146],{"className":4145},[3767],[568,4147,4149],{"className":4148,"style":3831},[3771],[568,4150],{},[568,4152],{"className":4153},[978,3755],[568,4155,2892],{"className":4156},[978],". Probe mit ",[568,4159,4161,4179],{"className":4160},[571],[568,4162,4164],{"className":4163},[575],[577,4165,4166],{"xmlns":579},[581,4167,4168,4176],{},[584,4169,4170,4172,4174],{},[587,4171,593],{},[595,4173,2071],{},[1454,4175,1565],{},[604,4177,4178],{"encoding":606},"x = 3",[568,4180,4182,4200],{"className":4181,"ariaHidden":612},[611],[568,4183,4185,4188,4191,4194,4197],{"className":4184},[616],[568,4186],{"className":4187,"style":685},[620],[568,4189,593],{"className":4190},[625,629],[568,4192],{"className":4193,"style":789},[633],[568,4195,2071],{"className":4196},[793],[568,4198],{"className":4199,"style":789},[633],[568,4201,4203,4206],{"className":4202},[616],[568,4204],{"className":4205,"style":1481},[620],[568,4207,1565],{"className":4208},[625],[568,4210,4212,4243],{"className":4211},[571],[568,4213,4215],{"className":4214},[575],[577,4216,4217],{"xmlns":579},[581,4218,4219,4240],{},[584,4220,4221,4223,4225,4227,4229,4231,4233,4235,4237],{},[587,4222,590],{"mathvariant":589},[1454,4224,1565],{},[595,4226,597],{},[1454,4228,1558],{},[587,4230,590],{"mathvariant":589},[595,4232,2071],{},[1454,4234,1816],{},[595,4236,1027],{},[1454,4238,4239],{},"7",[604,4241,4242],{"encoding":606},"|3 - 2| = 1 \u003C 7",[568,4244,4246,4265,4283,4301],{"className":4245,"ariaHidden":612},[611],[568,4247,4249,4252,4256,4259,4262],{"className":4248},[616],[568,4250],{"className":4251,"style":621},[620],[568,4253,4255],{"className":4254},[625],"∣3",[568,4257],{"className":4258,"style":634},[633],[568,4260,597],{"className":4261},[638],[568,4263],{"className":4264,"style":634},[633],[568,4266,4268,4271,4274,4277,4280],{"className":4267},[616],[568,4269],{"className":4270,"style":621},[620],[568,4272,3069],{"className":4273},[625],[568,4275],{"className":4276,"style":789},[633],[568,4278,2071],{"className":4279},[793],[568,4281],{"className":4282,"style":789},[633],[568,4284,4286,4289,4292,4295,4298],{"className":4285},[616],[568,4287],{"className":4288,"style":3224},[620],[568,4290,1816],{"className":4291},[625],[568,4293],{"className":4294,"style":789},[633],[568,4296,1027],{"className":4297},[793],[568,4299],{"className":4300,"style":789},[633],[568,4302,4304,4307],{"className":4303},[616],[568,4305],{"className":4306,"style":1481},[620],[568,4308,4239],{"className":4309},[625],". Mit ",[568,4312,4314,4332],{"className":4313},[571],[568,4315,4317],{"className":4316},[575],[577,4318,4319],{"xmlns":579},[581,4320,4321,4329],{},[584,4322,4323,4325,4327],{},[587,4324,593],{},[595,4326,2071],{},[1454,4328,1456],{},[604,4330,4331],{"encoding":606},"x = 0",[568,4333,4335,4353],{"className":4334,"ariaHidden":612},[611],[568,4336,4338,4341,4344,4347,4350],{"className":4337},[616],[568,4339],{"className":4340,"style":685},[620],[568,4342,593],{"className":4343},[625,629],[568,4345],{"className":4346,"style":789},[633],[568,4348,2071],{"className":4349},[793],[568,4351],{"className":4352,"style":789},[633],[568,4354,4356,4359],{"className":4355},[616],[568,4357],{"className":4358,"style":1481},[620],[568,4360,1456],{"className":4361},[625],[568,4363,4365,4391],{"className":4364},[571],[568,4366,4368],{"className":4367},[575],[577,4369,4370],{"xmlns":579},[581,4371,4372,4388],{},[584,4373,4374,4376,4378,4380,4382,4384,4386],{},[587,4375,590],{"mathvariant":589},[1454,4377,1456],{},[595,4379,597],{},[1454,4381,1558],{},[587,4383,590],{"mathvariant":589},[595,4385,2071],{},[1454,4387,1558],{},[604,4389,4390],{"encoding":606},"|0 - 2| = 2",[568,4392,4394,4413,4431],{"className":4393,"ariaHidden":612},[611],[568,4395,4397,4400,4404,4407,4410],{"className":4396},[616],[568,4398],{"className":4399,"style":621},[620],[568,4401,4403],{"className":4402},[625],"∣0",[568,4405],{"className":4406,"style":634},[633],[568,4408,597],{"className":4409},[638],[568,4411],{"className":4412,"style":634},[633],[568,4414,4416,4419,4422,4425,4428],{"className":4415},[616],[568,4417],{"className":4418,"style":621},[620],[568,4420,3069],{"className":4421},[625],[568,4423],{"className":4424,"style":789},[633],[568,4426,2071],{"className":4427},[793],[568,4429],{"className":4430,"style":789},[633],[568,4432,4434,4437],{"className":4433},[616],[568,4435],{"className":4436,"style":1481},[620],[568,4438,1558],{"className":4439},[625],", aber ",[568,4442,4444,4470],{"className":4443},[571],[568,4445,4447],{"className":4446},[575],[577,4448,4449],{"xmlns":579},[581,4450,4451,4467],{},[584,4452,4453,4455,4457,4459,4461,4463,4465],{},[1454,4454,1558],{},[595,4456,2052],{},[1454,4458,1456],{},[595,4460,899],{},[1454,4462,1816],{},[595,4464,2071],{},[1454,4466,1816],{},[604,4468,4469],{"encoding":606},"2 \\cdot 0 + 1 = 1",[568,4471,4473,4491,4509,4527],{"className":4472,"ariaHidden":612},[611],[568,4474,4476,4479,4482,4485,4488],{"className":4475},[616],[568,4477],{"className":4478,"style":1481},[620],[568,4480,1558],{"className":4481},[625],[568,4483],{"className":4484,"style":634},[633],[568,4486,2052],{"className":4487},[638],[568,4489],{"className":4490,"style":634},[633],[568,4492,4494,4497,4500,4503,4506],{"className":4493},[616],[568,4495],{"className":4496,"style":1662},[620],[568,4498,1456],{"className":4499},[625],[568,4501],{"className":4502,"style":634},[633],[568,4504,899],{"className":4505},[638],[568,4507],{"className":4508,"style":634},[633],[568,4510,4512,4515,4518,4521,4524],{"className":4511},[616],[568,4513],{"className":4514,"style":1481},[620],[568,4516,1816],{"className":4517},[625],[568,4519],{"className":4520,"style":789},[633],[568,4522,2071],{"className":4523},[793],[568,4525],{"className":4526,"style":789},[633],[568,4528,4530,4533],{"className":4529},[616],[568,4531],{"className":4532,"style":1481},[620],[568,4534,1816],{"className":4535},[625],", also nicht erfüllt, wie erwartet.",[559,4538,4540],{"id":4539},"typische-fehler","Typische Fehler",[4542,4543,4544,4732,4905],"ul",{},[1436,4545,4546,4547,4626,4627,4727,4728,4731],{},"Bei „größer als\" eine Doppelungleichung schreiben: ",[568,4548,4550,4575],{"className":4549},[571],[568,4551,4553],{"className":4552},[575],[577,4554,4555],{"xmlns":579},[581,4556,4557,4573],{},[584,4558,4559,4561,4563,4565,4567,4569,4571],{},[587,4560,590],{"mathvariant":589},[587,4562,593],{},[595,4564,899],{},[1454,4566,1816],{},[587,4568,590],{"mathvariant":589},[595,4570,1012],{},[1454,4572,1565],{},[604,4574,2370],{"encoding":606},[568,4576,4578,4599,4617],{"className":4577,"ariaHidden":612},[611],[568,4579,4581,4584,4587,4590,4593,4596],{"className":4580},[616],[568,4582],{"className":4583,"style":621},[620],[568,4585,590],{"className":4586},[625],[568,4588,593],{"className":4589},[625,629],[568,4591],{"className":4592,"style":634},[633],[568,4594,899],{"className":4595},[638],[568,4597],{"className":4598,"style":634},[633],[568,4600,4602,4605,4608,4611,4614],{"className":4601},[616],[568,4603],{"className":4604,"style":621},[620],[568,4606,2404],{"className":4607},[625],[568,4609],{"className":4610,"style":789},[633],[568,4612,1012],{"className":4613},[793],[568,4615],{"className":4616,"style":789},[633],[568,4618,4620,4623],{"className":4619},[616],[568,4621],{"className":4622,"style":1481},[620],[568,4624,1565],{"className":4625},[625]," bedeutet nicht ",[568,4628,4630,4658],{"className":4629},[571],[568,4631,4633],{"className":4632},[575],[577,4634,4635],{"xmlns":579},[581,4636,4637,4655],{},[584,4638,4639,4641,4643,4645,4647,4649,4651,4653],{},[595,4640,597],{},[1454,4642,1565],{},[595,4644,1012],{},[587,4646,593],{},[595,4648,899],{},[1454,4650,1816],{},[595,4652,1012],{},[1454,4654,1565],{},[604,4656,4657],{"encoding":606},"-3 > x + 1 > 3",[568,4659,4661,4682,4700,4718],{"className":4660,"ariaHidden":612},[611],[568,4662,4664,4667,4670,4673,4676,4679],{"className":4663},[616],[568,4665],{"className":4666,"style":1662},[620],[568,4668,597],{"className":4669},[625],[568,4671,1565],{"className":4672},[625],[568,4674],{"className":4675,"style":789},[633],[568,4677,1012],{"className":4678},[793],[568,4680],{"className":4681,"style":789},[633],[568,4683,4685,4688,4691,4694,4697],{"className":4684},[616],[568,4686],{"className":4687,"style":1145},[620],[568,4689,593],{"className":4690},[625,629],[568,4692],{"className":4693,"style":634},[633],[568,4695,899],{"className":4696},[638],[568,4698],{"className":4699,"style":634},[633],[568,4701,4703,4706,4709,4712,4715],{"className":4702},[616],[568,4704],{"className":4705,"style":3224},[620],[568,4707,1816],{"className":4708},[625],[568,4710],{"className":4711,"style":789},[633],[568,4713,1012],{"className":4714},[793],[568,4716],{"className":4717,"style":789},[633],[568,4719,4721,4724],{"className":4720},[616],[568,4722],{"className":4723,"style":1481},[620],[568,4725,1565],{"className":4726},[625],". Die Lösung besteht aus ",[656,4729,4730],{},"zwei"," getrennten Bereichen.",[1436,4733,4734,4735,4854,4855,979],{},"Bei der Fallunterscheidung das Ergebnis nicht mit der Fallbedingung schneiden. Im 2. Fall gilt ",[568,4736,4738,4759],{"className":4737},[571],[568,4739,4741],{"className":4740},[575],[577,4742,4743],{"xmlns":579},[581,4744,4745,4757],{},[584,4746,4747,4749,4751],{},[587,4748,593],{},[595,4750,1012],{},[3712,4752,4753,4755],{},[1454,4754,1816],{},[1454,4756,1565],{},[604,4758,3720],{"encoding":606},[568,4760,4762,4780],{"className":4761,"ariaHidden":612},[611],[568,4763,4765,4768,4771,4774,4777],{"className":4764},[616],[568,4766],{"className":4767,"style":1126},[620],[568,4769,593],{"className":4770},[625,629],[568,4772],{"className":4773,"style":789},[633],[568,4775,1012],{"className":4776},[793],[568,4778],{"className":4779,"style":789},[633],[568,4781,4783,4786],{"className":4782},[616],[568,4784],{"className":4785,"style":3748},[620],[568,4787,4789,4792,4851],{"className":4788},[625],[568,4790],{"className":4791},[920,3755],[568,4793,4795],{"className":4794},[3712],[568,4796,4798,4843],{"className":4797},[3762,3763],[568,4799,4801,4840],{"className":4800},[3767],[568,4802,4804,4818,4826],{"className":4803,"style":3772},[3771],[568,4805,4806,4809],{"style":3775},[568,4807],{"className":4808,"style":3780},[3779],[568,4810,4812],{"className":4811},[3784,3785,3786,3787],[568,4813,4815],{"className":4814},[625,3787],[568,4816,1565],{"className":4817},[625,3787],[568,4819,4820,4823],{"style":3796},[568,4821],{"className":4822,"style":3780},[3779],[568,4824],{"className":4825,"style":3804},[3803],[568,4827,4828,4831],{"style":3807},[568,4829],{"className":4830,"style":3780},[3779],[568,4832,4834],{"className":4833},[3784,3785,3786,3787],[568,4835,4837],{"className":4836},[625,3787],[568,4838,1816],{"className":4839},[625,3787],[568,4841,3824],{"className":4842},[3823],[568,4844,4846],{"className":4845},[3767],[568,4847,4849],{"className":4848,"style":3831},[3771],[568,4850],{},[568,4852],{"className":4853},[978,3755]," nur zusammen mit ",[568,4856,4858,4875],{"className":4857},[571],[568,4859,4861],{"className":4860},[575],[577,4862,4863],{"xmlns":579},[581,4864,4865,4873],{},[584,4866,4867,4869,4871],{},[587,4868,593],{},[595,4870,1027],{},[1454,4872,1558],{},[604,4874,3448],{"encoding":606},[568,4876,4878,4896],{"className":4877,"ariaHidden":612},[611],[568,4879,4881,4884,4887,4890,4893],{"className":4880},[616],[568,4882],{"className":4883,"style":1126},[620],[568,4885,593],{"className":4886},[625,629],[568,4888],{"className":4889,"style":789},[633],[568,4891,1027],{"className":4892},[793],[568,4894],{"className":4895,"style":789},[633],[568,4897,4899,4902],{"className":4898},[616],[568,4900],{"className":4901,"style":1481},[620],[568,4903,1558],{"className":4904},[625],[1436,4906,4907,4908,5023,5024,979],{},"Im 2. Fall das Minus nur vor den ersten Summanden setzen: ",[568,4909,4911,4945],{"className":4910},[571],[568,4912,4914],{"className":4913},[575],[577,4915,4916],{"xmlns":579},[581,4917,4918,4942],{},[584,4919,4920,4922,4924,4926,4928,4930,4932,4934,4936,4938,4940],{},[595,4921,597],{},[595,4923,2055],{"stretchy":880},[587,4925,593],{},[595,4927,597],{},[1454,4929,1558],{},[595,4931,2062],{"stretchy":880},[595,4933,2071],{},[595,4935,597],{},[587,4937,593],{},[595,4939,899],{},[1454,4941,1558],{},[604,4943,4944],{"encoding":606},"-(x - 2) = -x + 2",[568,4946,4948,4972,4993,5014],{"className":4947,"ariaHidden":612},[611],[568,4949,4951,4954,4957,4960,4963,4966,4969],{"className":4950},[616],[568,4952],{"className":4953,"style":621},[620],[568,4955,597],{"className":4956},[625],[568,4958,2055],{"className":4959},[920],[568,4961,593],{"className":4962},[625,629],[568,4964],{"className":4965,"style":634},[633],[568,4967,597],{"className":4968},[638],[568,4970],{"className":4971,"style":634},[633],[568,4973,4975,4978,4981,4984,4987,4990],{"className":4974},[616],[568,4976],{"className":4977,"style":621},[620],[568,4979,1558],{"className":4980},[625],[568,4982,2062],{"className":4983},[978],[568,4985],{"className":4986,"style":789},[633],[568,4988,2071],{"className":4989},[793],[568,4991],{"className":4992,"style":789},[633],[568,4994,4996,4999,5002,5005,5008,5011],{"className":4995},[616],[568,4997],{"className":4998,"style":1145},[620],[568,5000,597],{"className":5001},[625],[568,5003,593],{"className":5004},[625,629],[568,5006],{"className":5007,"style":634},[633],[568,5009,899],{"className":5010},[638],[568,5012],{"className":5013,"style":634},[633],[568,5015,5017,5020],{"className":5016},[616],[568,5018],{"className":5019,"style":1481},[620],[568,5021,1558],{"className":5022},[625],", nicht ",[568,5025,5027,5047],{"className":5026},[571],[568,5028,5030],{"className":5029},[575],[577,5031,5032],{"xmlns":579},[581,5033,5034,5044],{},[584,5035,5036,5038,5040,5042],{},[595,5037,597],{},[587,5039,593],{},[595,5041,597],{},[1454,5043,1558],{},[604,5045,5046],{"encoding":606},"-x - 2",[568,5048,5050,5071],{"className":5049,"ariaHidden":612},[611],[568,5051,5053,5056,5059,5062,5065,5068],{"className":5052},[616],[568,5054],{"className":5055,"style":1145},[620],[568,5057,597],{"className":5058},[625],[568,5060,593],{"className":5061},[625,629],[568,5063],{"className":5064,"style":634},[633],[568,5066,597],{"className":5067},[638],[568,5069],{"className":5070,"style":634},[633],[568,5072,5074,5077],{"className":5073},[616],[568,5075],{"className":5076,"style":1481},[620],[568,5078,1558],{"className":5079},[625],{"title":5081,"searchDepth":5082,"depth":5082,"links":5083},"",2,[5084,5085,5086],{"id":561,"depth":5082,"text":562},{"id":1538,"depth":5082,"text":1539},{"id":4539,"depth":5082,"text":4540},[5088,5090,5092,5094,5096,5098,5100,5102,5105,5107,5109,5111],{"lhs":5089,"rhs":746},"abs((a - r) - a)",{"lhs":5091,"rhs":746},"abs((a + r) - a)",{"lhs":5093,"rhs":1572},"abs(2*(-1) - 3)",{"lhs":5095,"rhs":1572},"abs(2*4 - 3)",{"lhs":5097,"rhs":1816},"abs(2*1 - 3)",{"lhs":5099,"rhs":1565},"abs(-4 + 1)",{"lhs":5101,"rhs":1565},"abs(2 + 1)",{"lhs":5103,"rhs":5104},"abs(1\u002F3 - 2)","2*(1\u002F3) + 1",{"lhs":5106,"rhs":1816},"abs(3 - 2)",{"lhs":5108,"rhs":4239},"2*3 + 1",{"lhs":5110,"rhs":1558},"abs(0 - 2)",{"lhs":5112,"rhs":1816},"2*0 + 1",null,"md","absolute-value-inequality","|x - a| \\leq r \\iff a - r \\leq x \\leq a + r","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|x - a| \\leq r \\iff a - r \\leq x \\leq a + r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.549em;vertical-align:-0.024em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⟺\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Falgebra\u002Fbetragsungleichung",[],[5124,5125,5126],"absolute-value","inequality-rules","triangle-inequality",{"title":548,"description":5081},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fbetragsungleichung","Der Abstand von x zu a ist höchstens r genau dann, wenn x im Intervall von a − r bis a + r liegt.",[5131,5132,5133,5134],"betrag","ungleichung","fallunterscheidung","intervall",[5136,5139,5142],{"symbol":593,"meaning":5137,"symbolHtml":5138},"Variable","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":600,"meaning":5140,"symbolHtml":5141},"Mittelpunkt des Lösungsintervalls","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord 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