化简：|2X+1|-|X-3|+|X-6|

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化简：|2X+1|-|X-3|+|X-6|
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化简：|2X+1|-|X-3|+|X-6|
化简：|2X+1|-|X-3|+|X-6|

化简：|2X+1|-|X-3|+|X-6|
1) -∞＜x＜-1/2 时,原式=-（2x+1)-[-(x-3)+[-(x-6)].
=-2x-1+x-3-x+6.
=-2x+2；
2）-1/2＜X＜3 时,原式=2x+1+x-3-x+6.
=2x+4；
3）3＜x＜6 时,原式=2x+1-(x-3)-x+6.
=10.
4) 6＜x 时,原式=2x+1-x+3+x-6.
=2x-2,

分别求出各个绝对值里面为零时的值分别为-1/2，3，6。然后按四种情况分别求出来。

当x≤-1/2
原式=-(2x+1)-(3-x)+(6-x)=2-2x
当-1/2原式=2x+1-(3-x)+6-x=2x+4
当3原式=2x+1-(x-3)+6-x=10
当x>6
原式=2x+1-(x-3)+x-6=2x-4

当x<-1/2时 原式=-(2x+1)-(3-x)+(6-x)
=-2x-1-3+X+6-x
=-2x+2
当-1/2<=x<3时 原式=2x+1-(3-x)+(6-x)
...

全部展开

当x<-1/2时 原式=-(2x+1)-(3-x)+(6-x)
=-2x-1-3+X+6-x
=-2x+2
当-1/2<=x<3时 原式=2x+1-(3-x)+(6-x)
=2x+1-3+x+6-x
=2x+4
当3<=x<6时 原式=2x+1-(x-3)+6-x
=10
当x>=6时 原式=2x+1-(x-3)+(x-6)
=2x-2

收起

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