## If $$|12x - 3| = |3x + 15|,$$ what is the value of $$x?$$

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### If $$|12x - 3| = |3x + 15|,$$ what is the value of $$x?$$

by Vincen » Fri Jan 28, 2022 4:47 am

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## Global Stats

If $$|12x - 3| = |3x + 15|,$$ what is the value of $$x?$$

(1) $$x > 0$$
(2) $$x$$ is an integer.

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### Re: If $$|12x - 3| = |3x + 15|,$$ what is the value of $$x?$$

by GMATGuruNY » Thu Feb 03, 2022 5:50 pm

00:00

A

B

C

D

E

## Global Stats

Vincen wrote:
Fri Jan 28, 2022 4:47 am
If $$|12x - 3| = |3x + 15|,$$ what is the value of $$x?$$

(1) $$x > 0$$
(2) $$x$$ is an integer
Case 1: Signs unchanged
12x-3 = 3x+15
9x = 18
x = 2

Case 2: Signs changed in ONE of the absolute values
12x-3 = -3x-15
15x = -12
x = -12/15 = -4/5

Statement 1: x > 0
Since only Case 1 is viable, x=2.
SUFFICIENT.

Statement 2: x is an integer
Since only Case 1 is viable, x=2.
SUFFICIENT.