If \(|2x - 7| > 17,\) which of the following must be true?

[Vincen]

If \(|2x - 7| > 17,\) which of the following must be true?

A. \(-5 < x < 0\)
B. \(0 < x < 12\)
C. \(-5 < x < 12\)
D. \(x < -5\) or \(x > 12\)
E. \(x < -12\) or \(x > 5\)

Answer: D

Source: e-GMAT

[Scott@TargetTestPrep]

If \(|2x - 7| > 17,\) which of the following must be true?

A. \(-5 < x < 0\)
B. \(0 < x < 12\)
C. \(-5 < x < 12\)
D. \(x < -5\) or \(x > 12\)
E. \(x < -12\) or \(x > 5\)

Answer: D

Solution:

We need to solve the inequality without the absolute value sign. If 2x - 7 is positive or 0, then |2x -7| = 2x - 7, and the inequality becomes:

2x - 7 > 17

2x > 24

x > 12

As we can see, the correct answer must be D. However, let’s finish the solution, solving for x when 2x - 7 is negative. In that case, |2x - 7| = -(2x - 7) = -2x + 7 and the inequality becomes:

-2x + 7 > 17

-2x > 10

x < -5

Answer: D