GMATprofessional21 wrote: ↑

Wed Aug 05, 2020 7:43 am

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

There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Given: |15 - 4x| = 2x
So, EITHER 15 - 4x = 2x OR 15 - 4x = -2x
Let's test each case.

Take: 15 - 4x = 2x
Add 4x to both sides: 15 = 6x
Solve: x = 15/6 = 5/2 = 2.5
Since we're told x ≠ 2.5, we can stop pursuing this case

Take: 15 - 4x = -2x
Add 4x to both sides: 15 = 2x
Solve: x = 15/2 = 7.5
NOTE: Since we've already seen that x = 2.5 is NOT a solution, we can be certain (without testing) that the correct answer must be x = 7.5

Answer: E

Cheers,
Brent

GMATprofessional21 wrote: ↑

Wed Aug 05, 2020 7:43 am

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

Solution:

If 15 - 4x is positive, we have:

2x = 15 - 4x

6x = 15

x = 2.5

If 15 - 4x is negative, we have:

2x = -15 + 4x

-2x = -15

x = 7.5

Since x ≠ 2.5, x must be 7.5.

Answer: E