︳x-1 ︳+︳ x+3︳﹥﹦6

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︳x-1︳+︳x+3︳﹥﹦6︳x-1︳+︳x+3︳﹥﹦6︳x-1︳+︳x+3︳﹥﹦6当x≥1时|x-1|+|x+3|≥6;x-1+x+3≥6;2x+2≥6;x≥2当-3≤x≤1时|x-1|+|x+3|

︳x-1 ︳+︳ x+3︳﹥﹦6
︳x-1 ︳+︳ x+3︳﹥﹦6

︳x-1 ︳+︳ x+3︳﹥﹦6
当x≥1时
|x-1|+|x+3|≥6;x-1+x+3≥6;2x+2≥6;x≥2
当-3≤x≤1时
|x-1|+|x+3|≥6;1-x+x+3≥6;4≥6;无解
当x≤-3时
|x-1|+|x+3|≥6;1-x+(-x-3)≥6;-2x-2≥6;-2x≥8;x≤-4
解得x≥2或者x≤-4

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