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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).

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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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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hope is a good thing, maybe the best of things. And no good thing ever dies.

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...

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?

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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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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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