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 \(x?\)

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

Answer: D

Source: Veritas Prep

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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.

The correct answer is D.
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