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

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Walkabout
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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   17 Dec 2012, 09:12
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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
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C
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Bunuel
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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   17 Dec 2012, 09:14
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Walkabout 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


\(\frac{4-x}{2+x}=x\);

\(4-x=x*(2+x)\);

\(4-x=2x+x^2\);

\(x^2+3x-4=0\).

As you can see there is no need to solve for x to answer the question.

Answer: C.
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   17 Dec 2012, 09:21
Simplify by keeping all the terms on side.
The equation becomes:

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

Now, expand the RHS of the equation:
(4-x) = 2x+x^2

Now, you see you already have a prt of the solution, a +ve x^2, so now, you need to move the LHS of the equation to the RHS and equate to 0:

0 = 2x+x^2-4+x

Simplify this further by adding 2x and x and voila!

x^2+3x-4 = 0

The answer is option C.
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   27 Oct 2015, 05:35
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feellikequitting 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



To solve any such question, I suggest that one should try to find one possible value of x that satisfies the given expression (4-x)/(2+x)=x

Try substituting Integer values in the range {-3, -2, -1, 0, 1, 2, 3}

The value x=1 satisfies the expression (4-x)/(2+x)=x

Hence, @x=1, x^2+3x-4 = 1^2+3*1-4 = 0

Answer: Option C
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   21 Jun 2016, 10:36
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feellikequitting 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


We start by simplifying the given equation, (4-x)/(2+x) = x. We first multiply both sides by 2+x. Thus we have:

4 – x = x(2 + x)

4 – x = 2x + x^2

4 = 3x + x^2

x^2 + 3x – 4 = 0

Before moving any further we note that we are not being asked for the value of x but rather the value of x^2 + 3x – 4.

So see that x^2 + 3x – 4 = 0.

The answer is C.
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   23 May 2017, 09:04
Walkabout 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


\(\frac{(4 - x)}{(2 + x)} = x\)

Or, \(4 - x = 2x +x^2\)

Or, \(x^2 + 3x - 4 = 0\)

Thus, the answer must be (C) 0
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   25 May 2017, 15:46
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Walkabout 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


We can simplify the given equation by first multiplying each side of the equation by (2 + x).

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

4 - x = x(2 + x)

4 - x = x^2 + 2x

x^2 + 3x - 4 = 0

Answer: C
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If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   Updated on: 28 Dec 2019, 07:35
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feellikequitting 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


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:
Show Spoiler
C

Originally posted by BrentGMATPrepNow on 28 Aug 2017, 14:03.
Last edited by BrentGMATPrepNow on 28 Dec 2019, 07:35, edited 1 time in total.
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   12 Mar 2018, 10:28
Walkabout 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



guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ? :?
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   12 Mar 2018, 11:59
dave13 wrote:
Walkabout 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



guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ? :?


Not quite.

On solving the given equation ,

\((4-x)/(2+x) = x\)
\(4-x = x*(2+x)\)
\(4-x = x^2 + 2x\)
\(0 = x^2 + 3x - 4\)

Hence 0.
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   13 Mar 2018, 00:56
Gladiator59 wrote:
dave13 wrote:
Walkabout 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



guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ? :?


Not quite.

On solving the given equation ,

\((4-x)/(2+x) = x\)
\(4-x = x*(2+x)\)
\(4-x = x^2 + 2x\)
\(0 = x^2 + 3x - 4\)

Hence 0.



hey Gladiator59 thanks ! What do mean by "Not quite." do you mean that it is not always that quadratics equal ZERO ? :)
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   13 Mar 2018, 01:10
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dave13 wrote:

hey Gladiator59 thanks ! What do mean by "Not quite." do you mean that it is not always that quadratics equal ZERO ? :)


Yeah dave13,

Precisely so. "Quadratics" may or may not equal 0. What does always equal zero is a "Quadratic equation".

So for example.

\(x^2 +3x - 4 = 0\) could be re-written as
\(x^2 + 3x -3 = 1\) ( adding 1 to both RHS and LHS )

Here the LHS is a "quadratic" expression that equals 1 (RHS)

More generally speaking .. quadratic expressions are parabolas and where the intersect the x-axis they equal zero.

Best,
Gladi
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   15 Sep 2019, 06:37
Walkabout 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


4-x = 2x + x^2
x^2+3x-4=0

IMO C

Posted from my mobile device
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   17 Nov 2021, 08:25
Walkabout wrote:
If \(\frac{(4 - x)}{(2 + x)} = x\), what is the value of \(x^2 + 3x -4\) ?

(A) -4
(B) -1
(C) 0
(D) 1
(E) 2
\(4 - x = 2x + x^2\)

So, \(x^2 + 3x - 4 = 0\), Answer will be (C)
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] New post   04 Jan 2024, 01:08
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