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If 3/2x-1=y, what is x in terms of y?
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30 Nov 2021, 06:26
30 Nov 2021, 06:26
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If \(\frac{3x}{2x-1}=y\), what is \(x\) in terms of \(y\)?
A. \(\frac{y-3}{2y}\)
B. \(\frac{2y}{y-3}\)
C. \(\frac{y}{2y-3}\)
D. \(\frac{y-3}{2y-3}\)
E. \(\frac{y}{y-3}\)
A. \(\frac{y-3}{2y}\)
B. \(\frac{2y}{y-3}\)
C. \(\frac{y}{2y-3}\)
D. \(\frac{y-3}{2y-3}\)
E. \(\frac{y}{y-3}\)
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Re: If 3/2x-1=y, what is x in terms of y?
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30 Nov 2021, 10:05
30 Nov 2021, 10:05
Carcass wrote:
If \(\frac{3x}{2x-1}=y\), what is \(x\) in terms of \(y\)?
A. \(\frac{y-3}{2y}\)
B. \(\frac{2y}{y-3}\)
C. \(\frac{y}{2y-3}\)
D. \(\frac{y-3}{2y-3}\)
E. \(\frac{y}{y-3}\)
A. \(\frac{y-3}{2y}\)
B. \(\frac{2y}{y-3}\)
C. \(\frac{y}{2y-3}\)
D. \(\frac{y-3}{2y-3}\)
E. \(\frac{y}{y-3}\)
Given: \(\frac{3}{2x-1}=y\)
Multiply both sides of the equation by \(2x-1\) to get: \(3x=y(2x-1)\)
Simplify: \(3x=2xy-y\)
Subtract \(2xy\) from both sides: \(3x-2xy=-y\)
Factor the left side: \(x(3-2y)=-y\)
Divide both sides of the equation by \(3-2y\) to get: \(\frac{-y}{3-2y}=x\)
When I checked the answer choices, I see that answer choice C closest resembles \(\frac{-y}{3-2y}\)
In fact, if we take the fraction \(\frac{-y}{3-2y}\) and multiply numerator and denominator by \(-1\), we get the equivalent fraction \(\frac{y}{-3+2y}\), and when we rearrange the denominator we get \(\frac{y}{2y-3}\)
Answer: C
gmatclubot
Re: If 3/2x-1=y, what is x in terms of y? [#permalink]
30 Nov 2021, 10:05
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