不等式|x-1|+|x+2|≥5的解集是________ 。

作者: tihaiku 人气: - 评论: 0
问题 不等式|x-1|+|x+2|≥5的解集是________ 。
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答案
解析 {x|x≤-3或x≥2}。解析:分三种情况讨论,①当x<-2时,原不等式等价于(1-x)+(-x-2)≥5,解得x≤-3;②当-2≤x≤1时,原不等式等价于(1-x)+(x+2)≥5,此时矛盾,不等式无解;③当x>1时,原不等式等价于(x-1)+(x+2)≥5,解得x≥2。综上,该不等式的解集为{x|x≤-3或x≥2}。

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