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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]

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Oct 2012, 08:27, edited 2 times in total.
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Re: OG Guide Problem 600-700 Level Question [#permalink]

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laythesmack23 wrote:
Pg. 172, OG Guide.

If [4-x][/2+x], what is the value of x^2+3x-4?

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

Please solve, and a step by step solution, thanks!


As you sited C as OA then I guess question should be:

If \(\frac{4-x}{2+x}=x\), what is the value of \(x^2+3x-4\)?

\(\frac{4-x}{2+x}=x\) --> \(4-x=x*(2+x)\) --> \(4-x=2x+x^2\) --> \(x^2+3x-4=0\).

Answer: C.
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Re: OG Guide Problem 600-700 Level Question [#permalink]

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New post 19 Apr 2012, 23:08
Bunuel wrote:
laythesmack23 wrote:
Pg. 172, OG Guide.

If [4-x][/2+x], what is the value of x^2+3x-4?

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

Please solve, and a step by step solution, thanks!


As you sited C as OA then I guess question should be:

If \(\frac{4-x}{2+x}=x\), what is the value of \(x^2+3x-4\)?

\(\frac{4-x}{2+x}=x\) --> \(4-x=x*(2+x)\) --> \(4-x=2x+x^2\) --> \(x^2+3x-4=0\).

Answer: C.


really silly question, is it because the question asks for the value of \(x^2+3x-4\) not x that we don't actually need to solve \(x^2+3x-4\) for x. I went right ahead to solve for x = (-4 or 1).
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Re: OG Guide Problem 600-700 Level Question [#permalink]

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New post 20 Apr 2012, 02:11
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catty2004 wrote:
Bunuel wrote:
laythesmack23 wrote:
Pg. 172, OG Guide.

If [4-x][/2+x], what is the value of x^2+3x-4?

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

Please solve, and a step by step solution, thanks!


As you sited C as OA then I guess question should be:

If \(\frac{4-x}{2+x}=x\), what is the value of \(x^2+3x-4\)?

\(\frac{4-x}{2+x}=x\) --> \(4-x=x*(2+x)\) --> \(4-x=2x+x^2\) --> \(x^2+3x-4=0\).

Answer: C.


really silly question, is it because the question asks for the value of \(x^2+3x-4\) not x that we don't actually need to solve \(x^2+3x-4\) for x. I went right ahead to solve for x = (-4 or 1).


Exactly so. The question asks about the value of \(x^2+3x-4\) while saying that \(\frac{4-x}{2+x}=x\). After simple algebraic manipulations we get that \(x^2+3x-4=0\), so there is no need to solve for \(x\).
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Re: If (4-x)/(2+x), what is the value of x^2+3x-4? [#permalink]

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New post 29 Oct 2012, 05:19
Hi Bunuel,
I solved for x to get -4 , 1 using the equation..
then substitutes in (4 – x)/(2 + x)= x only to find that both -4 and 1 satisfy (4 – x)/(2 + x)= x.

I then substituted -4 and 1 in x2 + 3x – 4 to get the answer 0 both the times...

Is this approach right?
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Re: If (4-x)/(2+x), what is the value of x^2+3x-4? [#permalink]

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New post 29 Oct 2012, 05:22
sachindia wrote:
Hi Bunuel,
I solved for x to get -4 , 1 using the equation..
then substitutes in (4 – x)/(2 + x)= x only to find that both -4 and 1 satisfy (4 – x)/(2 + x)= x.

I then substituted -4 and 1 in x2 + 3x – 4 to get the answer 0 both the times...

Is this approach right?


Yes, but no need to solve for x. Check here: if-4-x-2-x-what-is-the-value-of-x-2-3x-103932.html#p1076156
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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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New post 21 Oct 2014, 21:32
Bunuel wrote:
laythesmack23 wrote:
Pg. 172, OG Guide.

If [4-x][/2+x], what is the value of x^2+3x-4?

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

Please solve, and a step by step solution, thanks!


As you sited C as OA then I guess question should be:

If \(\frac{4-x}{2+x}=x\), what is the value of \(x^2+3x-4\)?

\(\frac{4-x}{2+x}=x\) --> \(4-x=x*(2+x)\) --> \(4-x=2x+x^2\) --> \(x^2+3x-4=0\).

Answer: C.



Hi Bunuel,

Your approach makes a lot of sense now that I see it - but I doubt I would be able to come up with this way of thinking in a new problem.

When I saw the problem text "If x= *xyz*, what is the value of x^2 + 3x -4?", my first thought was to just put the *xyz* into the equation and solve: *xyz*^2 +3(*xyz*) -4.

After calculating that to the end, I get D, =1 as a solution.

My question: what do you think has to be the trigger for me in this question to right away notice to NOT go down that road? What is the thinking pattern that is used here that I can transfer to other problems in order to make sure to not make that mistake again?


Hope I'm clear, thanks in advance!


Cheers
Christian
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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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New post 22 Oct 2014, 00:10
christian1904 wrote:
Bunuel wrote:
laythesmack23 wrote:
Pg. 172, OG Guide.

If [4-x][/2+x], what is the value of x^2+3x-4?

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

Please solve, and a step by step solution, thanks!


As you sited C as OA then I guess question should be:

If \(\frac{4-x}{2+x}=x\), what is the value of \(x^2+3x-4\)?

\(\frac{4-x}{2+x}=x\) --> \(4-x=x*(2+x)\) --> \(4-x=2x+x^2\) --> \(x^2+3x-4=0\).

Answer: C.



Hi Bunuel,

Your approach makes a lot of sense now that I see it - but I doubt I would be able to come up with this way of thinking in a new problem.

When I saw the problem text "If x= *xyz*, what is the value of x^2 + 3x -4?", my first thought was to just put the *xyz* into the equation and solve: *xyz*^2 +3(*xyz*) -4.

After calculating that to the end, I get D, =1 as a solution.

My question: what do you think has to be the trigger for me in this question to right away notice to NOT go down that road? What is the thinking pattern that is used here that I can transfer to other problems in order to make sure to not make that mistake again?


Hope I'm clear, thanks in advance!


Cheers
Christian


Given expression (\(\frac{4-x}{2+x}=x\)) is not in its simplest form, so I decided to simplify it and while simplifying got the answer right away.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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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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]

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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]

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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:
[Reveal] Spoiler:
C


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