What is the value of x? $|x+2|+|x-3| = |2x+3|$

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by GMATGuruNY » Mon Apr 23, 2018 2:59 am

Gmat_mission wrote:What is the value of x? $$|x+2|+|x-3|=|2x+3|$$ A. -5
B. -2
C. 1
D. 4
E. 7

We can PLUG IN THE ANSWERS, which represent the value of x.

E: x=7
Substituting x=7 into |x+2|+|x-3|=|2x+3|, we get:
|7+2|+|7-3|=|2*7 + 3|
9 + 4 = 17
13 = 17.
Doesn't work.
Eliminate E.

D: x=4
Substituting x=4 into |x+2|+|x-3|=|2x+3|, we get:
|4+2|+|4-3|=|2*4 + 3|
6 + 1 = 11
7 = 11.
Doesn't work.
Eliminate D.

C: x=1
Substituting x=1 into |x+2|+|x-3|=|2x+3|, we get:
|1+2|+|1-3|=|2*1 + 3|
3 + 2 = 5
5 = 5.
Success!

The correct answer is C.

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