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.
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OG2016 PS If (4 - x)/(2 + x) = x
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lionsshare
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Last edited by lionsshare on Mon Aug 28, 2017 1:15 pm, edited 1 time in total.
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Brent@GMATPrepNow
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Given: (4 - x)/(2 + x) = xlionsshare 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
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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Jay@ManhattanReview
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We are given that (4 - x)/(2 + x) = x. And we have to reach x^2 + 3x -4 from the given expression.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.
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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Matt@VeritasPrep
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(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
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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Matt@VeritasPrep
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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 ...
The GMAC can be so mean ...
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Jeff@TargetTestPrep
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We can simplify the given equation: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
(4 - x)/(2 + x) = x
4 - x = 2x + x^2
0 = x^2 + 3x - 4
Answer:C
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saminazahid2002
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(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.
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.
