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

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If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   16 Jun 2020, 03:28
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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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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   16 Jun 2020, 03:28
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   16 Jun 2020, 05:22
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Carcass 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: C

Cheers,
Brent
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   Updated on: 17 Jun 2020, 18:27
I am confused about question. Don't we have to find roots? we won't apply quadratic equation formula?
GreenlightTestPrep wrote:
The question asks us to find the value of x² + 3x - 4
Notice that this in a algebraic EXPRESSION and not an algebraic EQUATION.

Most algebraic EXPRESSIONS can have infinitely many values.

For example, if x = 0, then x² + 3x - 4 = 0² + 3(0) - 4 = -4
If x = 2, then x² + 3x - 4 = 2² + 3(2) - 4 = 6
If x = 10, then x² + 3x - 4 = 10² + 3(10) - 4 = 126
If x = -5, then x² + 3x - 4 = (-5)² + 3(-5) - 4 = 6
etc

So, on it's own, the algebraic EXPRESSION x² + 3x - 4 has no particular value. In fact, the value of x² + 3x - 4 depends exclusively on the value of x.


The EQUATION x² + 3x - 4 = 0 is different.
When we're asked to solve this equation, we're looking for a value(s) of x such that the algebraic EXPRESSION x² + 3x - 4 has the value of 0.

Cheers,
Brent

Originally posted by Farina on 16 Jun 2020, 17:44.
Last edited by Farina on 17 Jun 2020, 18:27, 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   17 Jun 2020, 17:28
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(4-x)/)(2+x) = x

4 - x = 2x + x^2

2x + x^2 = 4 - x

x^2 + 3x - 4 = 0

And this is the question.
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   05 Nov 2020, 17:31
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Carcass 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)/(2+x)=x --> 4-x = 2x+x^2 --> 4 = x^2 + 3x.

If we substitute x^2 + 3 as 4 we get 4-4 = 0.

Hence option C is the answer.
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   06 Nov 2020, 17:06
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Another way you could figure this out fairly quickly without having to use much brain power is plugging in the answer choices into the first equation and seeing which of the values you plug in for X hold true.
For example:
The first equation is: (4-x) / (2+x) = x.
A) -4
Let's plug in -4 to start with...
(4+4) / (2-4) = -4 ?
8 / -2 = -4 Which is correct.
So now you know your x-value.
Be careful because the question asks for the value for x^2 + 3x - 4, NOT the value of x!
Plugging in x = -4 to the equation gets us x^2 + 3x - 4 = 0 which is the answer (C).

Saves a good bit of time if you're quick to utilize tricks like this and don't really know how to work it out using algebra or don't want to use the algebra.
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   13 Apr 2024, 01:26
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Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink]
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