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If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?

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If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?  [#permalink]

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New post 06 Dec 2018, 04:17
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Re: If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?  [#permalink]

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New post 06 Dec 2018, 04:24
4x/(x^2-3x) - 2/7=0
which means 4x/(x^2-3x)=2/7
Since x>0, 4x/x(x-3)=2/7
Cancelling out x from numerator and denominator, we get 4/(x-3)= 2/7
Solving for x gives 2x-6=28
Hence x=17

Hence B
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If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?  [#permalink]

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New post Updated on: 07 Dec 2018, 06:34
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Bunuel wrote:
If x > 0 and \(\frac{4x}{(x^2 -3x)} - \frac{2}{7} = 0\) what is the value of x?

A. 15
B. 17
C. 19
D. 21
E. 23


GIVEN: \(\frac{4x}{(x^2 -3x)} - \frac{2}{7} = 0\)
Add 2/7 to both sides to get: \(\frac{4x}{(x^2 -3x)}= \frac{2}{7}\)
Cross multiply to get: (2)(x² - 3x) = (7)(4x)
Expand to get: 2x² - 6x = 28x
Subtract 28x from both sides to get: 2x² - 34x = 0
Factor to get: 2x(x - 17) = 0
So, EITHER x = 0 OR x = 17

Since we're told x > 0, we can conclude that x = 17

Answer: B

Cheers,
Brent
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Originally posted by GMATPrepNow on 06 Dec 2018, 07:36.
Last edited by GMATPrepNow on 07 Dec 2018, 06:34, edited 1 time in total.
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Re: If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?  [#permalink]

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New post 07 Dec 2018, 06:29
GMATPrepNow wrote:
Bunuel wrote:
If x > 0 and \(\frac{4x}{(x^2 -3x)} - \frac{2}{7} = 0\) what is the value of x?

A. 15
B. 17
C. 19
D. 21
E. 23


GIVEN: \(\frac{4x}{(x^2 -3x)} - \frac{2}{7} = 0\)

Cross multiply to get: (2)(x² - 3x) = (7)(4x)
Expand to get: 2x² - 6x = 28x
Subtract 28x from both sides to get: 2x² - 34x = 0
Factor to get: 2x(x - 17) = 0
So, EITHER x = 0 OR x = 17

Since we're told x > 0, we can conclude that x = 17

Answer: B

Cheers,
Brent


Dear GMATPrepNow Brent

This problem stimulates a question. Suppose the question does not say x >0. Can x=0 be a valid solution? I do not think so as it will turn the original fraction into 0/0 which is undefined. My take away that I need to refer to orginal question after finding solution.

Is my thinking right. What do you think?

Thanks in advance
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Re: If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?  [#permalink]

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New post 07 Dec 2018, 06:36
Top Contributor
Mo2men wrote:
Dear GMATPrepNow Brent

This problem stimulates a question. Suppose the question does not say x >0. Can x=0 be a valid solution? I do not think so as it will turn the original fraction into 0/0 which is undefined. My take away that I need to refer to orginal question after finding solution.

Is my thinking right. What do you think?

Thanks in advance


You're absolutely right; x = 0 cannot be a valid solution.
So, regardless of the proviso that x>0, the ONLY solution is x = 17

Cheers,
Brent
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Re: If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?  [#permalink]

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Re: If x > 0 and 4x/(x^2 −3x) − 2/7 = 0 what is the value of x?   [#permalink] 10 Jan 2020, 04:57
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