Question

丨3x+2丨-丨2x-7丨化简

丨3x+2丨-丨2x-7丨化简

Answer 1

先找零点，

3x+2=0，得x = -2/3.

2x-7 = 0，得x = 7/2.

以这两个点分为3段，分别化简。

x ＜ -2/3，

丨3x+2丨-丨2x-7丨

= -(3x+2) + (2x-7) 

= - x - 9

 -2/3 ≤ x  ≤  7/2，

丨3x+2丨-丨2x-7丨

= (3x+2) + (2x-7) 

= 5x - 5

x ＞7/2，

丨3x+2丨-丨2x-7丨

= (3x+2) - (2x-7) 

= x+9

函数图象 供参考

Answer 2

丨3x+2丨-丨2x-7丨化简
分点为 -2/3 7/2

当 x <= -2/3 时
丨3x+2丨-丨2x-7丨
= -3x-2 - 7+ 2x
= -x - 9

当 - 2/3<x <= 7/2 时
丨3x+2丨-丨2x-7丨
= 3x + 2 - 7+ 2x
= 5x -5

当 x > 7/2 时
丨3x+2丨-丨2x-7丨
= 3x + 2 -2x + 7
= x +9

Answer 3

丨3x+2丨-丨2x-7丨

=1/3|x+2/3|-1/2|x-7/2|
(1) x>=7/2
3x+2-(2x-7)
=x+9
(2)x<=-2/3
-(3x+2)+(2x-7)
=-x-9
-2/3<x<7/2
(3x+2)+(2x-7)
=5x-5

Answer 4

当x>=3.5时，原式=3x+2-2x+7=x+9
当-2/3<x<3.5时，原式=3x+2-7+2x=5x-5
当x<-2/3时，原式=-3x-2-7+2x=-x-9