4/x + 3x = 3(x-12) : GMAT Problem Solving (PS)

4/x + 3x = 3(x-12)

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4/x + 3x = 3(x-12) [#permalink]

22 Aug 2012, 11:17

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Question Stats:

64% (01:30) correct

35% (00:34) wrong

based on 3 sessions

4/x + 3x = 3(x-12)

A. -9
B. -1/3
C. -1/9
D. 1/9
E. 9

[Reveal] Spoiler: OA

Last edited by feellikequitting on 22 Aug 2012, 16:51, edited 1 time in total.

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Re: 4/X + 3x = 3(x-12) [#permalink]

22 Aug 2012, 11:58

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laythesmack23 wrote:

A -9
B -1/3
C -1/9
D 1/9
E 9

Explain your Answer!!!

You have given the OA as B, but you can see by plugging x = -1/3 into the equation that B is not the right answer.

We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:

(4/X) + 3x = 3(x-12)
(4/x) + 3x = 3x - 36
4 + 3x^2 = 3x^2 - 36x
4 = -36x
-1/9 = x

and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
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Re: 4/X + 3x = 3(x-12) [#permalink]

22 Aug 2012, 16:51

Dude, you're awesome! Yeah, it was my mistake, correct answer is C! I see what you did, you did it much easier than the mgmat website.

When simplifying the equation like 4/X + 3X= 3X-36, to remove the denominator, we multiply with 3X,by both sides, is this correct? And this gives us 4+3x^2=3x^2-36 (are you multiplying by X on the left side to both sides? to square both 3X's?, I'm assuming this isolates the problem to 4=-36? then you divide by 4.

I don't follow why this becomes

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Re: 4/X + 3x = 3(x-12) [#permalink]

22 Aug 2012, 19:04

laythesmack23 wrote:

How about instead of multiplying the equation by 'x', why not subtract '3x' from both sides first => 4/x = -36
Then multiply both sides by 'x' => 4 = -36x
Divide both sides by '-36' and simplify

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Re: 4/x + 3x = 3(x-12) [#permalink]

22 Aug 2012, 23:10

laythesmack23 wrote:

4/x + 3x = 3(x-12)

A. -9
B. -1/3
C. -1/9
D. 1/9
E. 9

\frac{4}{x} + 3x = 3(x-12) --> \frac{4}{x} + 3x = 3x-36 --> 3x cancels out: \frac{4}{x}=-36 --> x=-\frac{4}{36}=-\frac{1}{9}.

Answer: C.
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Re: 4/x + 3x = 3(x-12) [#permalink]

08 Dec 2012, 05:36

\frac{4}{x}+ 3x = 3x-36
\frac{4}{x} = 3x-3x-36
\frac{4}{x} = -36
-36x = 4
x=-\frac{1}{9}

Answer: -1/9

Re: 4/x + 3x = 3(x-12) [#permalink] 08 Dec 2012, 05:36

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4/x + 3x = 3(x-12)

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4/x + 3x = 3(x-12)

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