SOLUTION: For what real values of x is |x|+|x+2|+|2-x|‹=8

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Question 1038920: For what real values of x is |x|+|x+2|+|2-x|‹=8
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
This inequality has three critical values of 2, 0, and -2. These critical values cut the real number line into four intervals. Determine the sign of each absolute value expression in each interval and then check the truth or falsity of the inequality.

(-infinity, -2]
pick x=-3
3%2B1%2B5
8%3C=8
TRUE

[-2, 0]
pick -1
1%2B1%2B3%3C=8
5%3C=8
TRUE

[0, 2]
pick 1 for x.
1%2B3%2B0%3C=8
4%3C=8
TRUE

[2, infinity)
pick x=4.
4%2B6%2B2%3C=8
12%3C=8
FALSE

Solution is highlight%28highlight%28x%3C=2%29%29.

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
For what real values of x is |x|+|x+2|+|2-x|‹=8
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Figure. Plots y = |x|+|x+2|+|2-x| and y = 8.

Solution is |x| <= 8%2F3.