If x ≠2.5 and 2x = |15 - 4x|, then x = ?

[hansoo]

If x ≠ 2.5 and 2x = |15 - 4x|, then x =

a) 3.5
b) 4.5
c) 5.5
d) 6.5
e) 7.5

[truplayer256]

2x=|15-4x|

Case 1:

-2x=15-4x

x=15/2=7.5

Case 2:

2x=15-4x

x=15/6=5/3

E

[hansoo]

Good work! The official answer is E.

A video explanation can be viewed here: GMAT Video Explanation

[Scott@TargetTestPrep]

If x ≠ 2.5 and 2x = |15 - 4x|, then x =

a) 3.5
b) 4.5
c) 5.5
d) 6.5
e) 7.5

For this absolute value question, we must consider two cases: (1) when (15 - 4x) is positive and (2) when (15 - 4x) is negative.

Case 1. When 15 - 4x is positive, we have:

2x = 15 - 4x

6x = 15

x = 15/6 = 2.5

Case 2. When 15 - 4x is negative, we have:

2x = -15 + 4x

15 = 2x

7.5 = x

Since x is not 2.5, x must be 7.5.

Answer: E