Question

化简|x+6|-|x-2|=?

Answer 1

分三段考虑：
|x+6|-|x-2|=
{x+6-(x-2)=8,x≥2;
{x+6+x-2=2x+4,-6<x<2;
{-(x+6)+x-2=-8,x≤-6.

Answer 2

首先要讨论X的取值范围
1:）X小于2，则为2-X+（6—X）=8—2X
2）X大于等于2小于等于6，则为X-2+（6-X）=2X+4
3)X大于6，则为（X-2）+（X-6）=2X-8

Answer 3

x ≤ -6 :
|x + 6| - |x - 2| = -(x + 6) + (x - 2) = -8
-6 < x < 2 :
|x + 6| - |x - 2| = (x + 6) + (x - 2) = 2x + 4
x ≥ 2 :
|x + 6| - |x - 2| = (x + 6) - (x - 2) = 8

Answer 4

case 1: x≤-6
|x+6|-|x-2|
=-(x+6)+(x-2)
=-8
case 2: -6<x<2
|x+6|-|x-2|
=(x+6)+(x-2)
=2x+4
case 3: x≥2
|x+6|-|x-2|
=(x+6)-(x-2)
=8
ie
|x+6|-|x-2|
=-8 ; x≤-6
=2x+4 ; -6<x<2
=8 ; x≥2