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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Which of the following is the solution set for the inequalit tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Which of the following is the solution set for the inequalit ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] Which of the following is the solution set for the inequality 0 < |x|-2x < 3? A. -1 < x < 0 B. 0 < x < 1 C. 1 < x < 2 D. 2 < x < 3 E. 3 < x < 4 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

Which of the following is the solution set for the inequality 0 < |x|-2x < 3?

A. -1 < x < 0
B. 0 < x < 1
C. 1 < x < 2
D. 2 < x < 3
E. 3 < x < 4
We can PLUG IN THE ANSWERS, which represent the range of x.

A: -1 < x < 0
Plugging x=-0.5 into the given inequality, we get:
0 < |-0.5| - 2(-0.5) < 3
0 < 0.5 + 1 < 3
0 < 1.5 > 3
Since x=-0.5 is a valid solution, the correct answer must include x=-0.5 within its range.
Eliminate B, C, D and E.

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By definition, if x â‰¥ 0, then |x| = x and if x < 0, |x| = -x.

If x â‰¥ 0, then 0 < |x|-2x<3 is equivalent to 0 < x - 2x < 3 or 0 < -x < 3.
So, -3 < x < 0, which does not satisfy the assumption x â‰¥ 0.
If x < 0, then 0<|x|-2x<3 is equivalent to 0 < -x -2x < 3 or 0 < -3x < 3.
Then -1 < x < 0, which satisfies the assumption x < 0.
Thus, the solution set is -1 < x < 0.

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