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Multiplying which of the following by the nonzero number (5 - 2x)/7

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Multiplying which of the following by the nonzero number (5 - 2x)/7  [#permalink]

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New post 22 Nov 2019, 03:31
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A
B
C
D
E

Difficulty:

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Question Stats:

63% (00:52) correct 38% (01:01) wrong based on 16 sessions

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Re: Multiplying which of the following by the nonzero number (5 - 2x)/7  [#permalink]

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New post 22 Nov 2019, 08:25
Top Contributor
Bunuel wrote:
Multiplying which of the following by the nonzero number \(\frac{5-2x}{7}\) will give you a product of \(-1\)?

A. \(\frac{7}{5-2x}\)

B. \(\frac{-7}{2x-5}\)

C. \(\frac{7}{2x-5}\)

D. \(\frac{2x-5}{7}\)

E. \(7(2x-5)\)


Useful property: \((\frac{b}{c})(\frac{c}{b})=1\)

Let \(k\) = the desired value.

So, we want: \((\frac{5-2x}{7})(k) = -1\)

Multiply both sides by \(\frac{7}{5-2x}\) to get: : \((\frac{7}{5-2x})(\frac{5-2x}{7})(k) = (-1)(\frac{7}{5-2x})\)

Apply above property to get: \((1)(k) = (-1)(\frac{7}{5-2x})\)

From here, it's useful to scan the answer choices to see what format they want.

It looks like we can apply another use property, which says \((-1)(a - b) = b - a\)

So, take the last given equation and rewrite it as follows: \(k = (\frac{1}{-1})(\frac{7}{5-2x})\)

Multiply the numerators and denominators to get: \(k=\frac{7}{2x-5}\)

Answer: C

Cheers,
Brent
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Re: Multiplying which of the following by the nonzero number (5 - 2x)/7   [#permalink] 22 Nov 2019, 08:25
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Multiplying which of the following by the nonzero number (5 - 2x)/7

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