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

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4/x + 3x = 3(x-12) [#permalink]

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22 Aug 2012, 10:17
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Difficulty:

5% (low)

Question Stats:

83% (01:31) correct 17% (00:46) wrong based on 94 sessions

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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, 15:51, edited 1 time in total.
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Re: 4/X + 3x = 3(x-12) [#permalink]

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22 Aug 2012, 10:58
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Expert's post
laythesmack23 wrote:
A -9
B -1/3
C -1/9
D 1/9
E 9

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]

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22 Aug 2012, 15:51
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]

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22 Aug 2012, 18:04
laythesmack23 wrote:
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

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]

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22 Aug 2012, 22:10
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: $$\frac{4}{x}=-36$$ --> $$x=-\frac{4}{36}=-\frac{1}{9}$$.

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Re: 4/x + 3x = 3(x-12) [#permalink]

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08 Dec 2012, 04:36
$$\frac{4}{x}+ 3x = 3x-36$$
$$\frac{4}{x} = 3x-3x-36$$
$$\frac{4}{x} = -36$$
$$-36x = 4$$
$$x=-\frac{1}{9}$$

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Re: 4/x + 3x = 3(x-12)   [#permalink] 08 Dec 2012, 04:36
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