SOLUTION: Trying to solve: 2|x-8|+2<=12 I keep getting 1<=x<=13 but I know that is not right. The answer is 3<=x<=13 but I just can't see how we get that. Thx!

Question 503811: Trying to solve: 2|x-8|+2<=12
I keep getting 1<=x<=13 but I know that is not right.
The answer is 3<=x<=13 but I just can't see how we get that.
Thx!
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Consider:
2|x-8|+2<=12
as TWO different problems:
.
First problem:
2(x-8)+2<=12
Second problem:
2(-(x-8))+2<=12
.
Solving First:
2(x-8)+2<=12
2x-16+2<=12
2x-14<=12
2x<=26
x<=13
.
Solving Second:
2(-(x-8))+2<=12
2(-x+8)+2<=12
(-2x+16)+2<=12
-2x+18<=12
-2x<=-6
2x>=6 (notice we flipped the less than sign)
x>=3
.
answer:
3<=x<=13

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