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OG2016 PS If (4 - x)/(2 + x) = x

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by Brent@GMATPrepNow » Mon Aug 28, 2017 12:56 pm
lionsshare wrote:If (4 - x)/(2 + x) = x, what is the value of x² + 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
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by Jay@ManhattanReview » Tue Aug 29, 2017 8:49 pm
lionsshare wrote: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

Anyone, please share the solution for this problem. Thanks.
We are given that (4 - x)/(2 + x) = x. And we have to reach x^2 + 3x -4 from the given expression.

Let's manipulated the given expression.

(4 - x)/(2 + x) = x

(4 - x) = x*(2 + x); cross-multiplying (2 + x)

4 - x = 2x + x^2; opening the parenthesis

x^2 + 3x - 4 = 0

The value of the asked expression is 0.

The correct answer: C

Hope this helps!

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by Matt@VeritasPrep » Wed Aug 30, 2017 5:56 pm
(4 - x) / (2 + x) = x

multiply both sides by (2 + x):

4 - x = x * (2 + x), or

4 - x = x² + 2x

add x to both sides:

4 = x² + 3x

subtract 4 from both sides:

0 = x² + 3x - 4

so x² + 3x - 4 = 0, and we're done
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by Matt@VeritasPrep » Wed Aug 30, 2017 5:57 pm
By the way, in case anyone out there is scratching his/her head at this answer: REMEMBER THAT THE PROBLEM ISN'T ASKING US TO SOLVE FOR X :)

The GMAC can be so mean ...
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by Jeff@TargetTestPrep » Sat Sep 02, 2017 6:27 am
lionsshare wrote: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
We can simplify the given equation:

(4 - x)/(2 + x) = x

4 - x = 2x + x^2

0 = x^2 + 3x - 4

Answer:C

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OG2016 PS If (4 - x)/(2 + x) = x

by saminazahid2002 » Sat Sep 02, 2017 11:03 am
(4 - x)/(2 + x) = x

Multiplying both sides by (2+x)
(4 - x) = x(2+x)
4 - x = 2x + x² (Distributive property)
4 - x + x= 2x + x² + x (Adding x on both sides)
4 = 2x + x² + x
4 = 2x + x + x² (Combining Like Terms)
4 = 3x + x²
4 - 4 = 3x + x² - 4 (Subtracting 4 on both sides)
0 = x² + 3x - 4
x² + 3x - 4 = 0

Therefore, x² + 3x - 4 is equal to zero, hence, Option C is correct.
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