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# The inequality

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The inequality [#permalink]  17 Sep 2017, 03:59
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Question Stats:

100% (01:59) correct 0% (00:00) wrong based on 5 sessions

The inequality |8 - 2x| < 3y - 9 is equivalent to which of the following?

A. $$2x < \frac{(17 - 3Y)}{2}$$

B. 3y + 2x > 1

C. 6y – 2 < 2x

D. 1 – y < 2x < 17 + y

E. 3y – 1 > 2x > 17 – 3y
[Reveal] Spoiler: OA

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Re: The inequality [#permalink]  18 Sep 2017, 00:10
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|8-2x| is equal to 8-2x when 8-2x >=0 and equal to 2x-8 when 8-2x<0. Thus, we can rewrite the disequality as two, i.e. 8-2x<3y-9 and 2x-8<3y-9. Rearranging and having looked at the answer choices, it is meaningful to explicit the term 2x as 2x>17-3y from the first disequality and 2x<3y-1 from the second one. This can be rewritten as 3y-1>2x>3y-17. Thus, the answer is E!
Re: The inequality   [#permalink] 18 Sep 2017, 00:10
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