SOLUTION: Solve the inequality |3x-6| ≥ |4-x|.

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Question 1186194: Solve the inequality |3x-6| ≥ |4-x|.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Expression on the left changes sign around 2.
Expression on the right changes sign around 4.

The intervals on the number line are to be checked.
system%28x%3C=2%2C2%3C=x%3C=4%2C4%3C=x%29.


(1)
-3x%2B6%3E=4-x
6-4%3E=-x%2B3x
2%3E=2x
x%3C=1

(2)
3x-6%3E=4-x
4x%3E=10
x%3E=5%2F2

(3)
3x-6%3E=-4%2Bx
4x%3E=-10
x%3E=-5%2F2

Each of those need to be checked to see if they work in the original inequality.

The work above contains a mistake.
The real solution is for x%3C=1 OR x%3E=2.5.