不等式2x-1的绝对值+x+2的绝对值<4的解集为
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不等式2x-1的绝对值+x+2的绝对值<4的解集为
![不等式2x-1的绝对值+x+2的绝对值<4的解集为](/uploads/image/z/18565379-35-9.jpg?t=%E4%B8%8D%E7%AD%89%E5%BC%8F2x-1%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%2Bx%2B2%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%EF%BC%9C4%E7%9A%84%E8%A7%A3%E9%9B%86%E4%B8%BA)
|2x-1|+|x+2|<4
|2x-1|<4-|x+2|
把绝对值打开,出现4种情况:
(1)2x-1<4-(x+2)
2x-1<4-x-2
x<1
(2) 2x-1<4-[-(x+2)]
2x-1<4+x+2
x<7
(3)-2x+1<4-(x+2)
-2x+1<4-x-2
x>-1
(4)-2x+1<4-[-(x+2)]
-2x+1<4+x+2
x>-5/3
综上所述,x的范围是 -1<x<1
|2x-1|<4-|x+2|
把绝对值打开,出现4种情况:
(1)2x-1<4-(x+2)
2x-1<4-x-2
x<1
(2) 2x-1<4-[-(x+2)]
2x-1<4+x+2
x<7
(3)-2x+1<4-(x+2)
-2x+1<4-x-2
x>-1
(4)-2x+1<4-[-(x+2)]
-2x+1<4+x+2
x>-5/3
综上所述,x的范围是 -1<x<1