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

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Math Expert
Joined: 02 Sep 2009
Posts: 59573
Multiplying which of the following by the nonzero number (5 - 2x)/7  [#permalink]

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22 Nov 2019, 03:31
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Question Stats:

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

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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. $$7(2x-5)$$

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

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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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