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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4?

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by AAPL » Sat Sep 11, 2021 6:51 am
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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4?

A. -4
B. -1
C. 0
D. 1
E. 2

OA C
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4?

by Brent@GMATPrepNow » Sat Sep 11, 2021 11:53 am
AAPL wrote: ↑
Sat Sep 11, 2021 6:51 am
 Official Guide

If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4?

A. -4
B. -1
C. 0
D. 1
E. 2

OA C
Given: (4 - x)/(2 + x) = x
Eliminate the fraction by multiplying both sides by (2 + x) to get: (4 - x) = (x)(2 + x)
Expand: 4 - x = 2x + x²
Add x to both sides: 4 = x² + 3x
Subtract 4 from both sides: 0 = x² + 3x - 4

PERFECT! The question asks us to find the value of x² + 3x - 4, and we just showed that the expression equals 0

Answer: C
Brent Hanneson - Creator of GMATPrepNow.com
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