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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Which of the following is the solution set for the inequality 0<|x|-2x  [#permalink]

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28 Mar 2019, 01:42
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Difficulty:

35% (medium)

Question Stats:

71% (02:02) correct 29% (02:12) wrong based on 103 sessions

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[GMAT math practice question]

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

$$A. -1<x<0$$
$$B. 0<x<1$$
$$C. 1<x<2$$
$$D. 2<x<3$$
$$E. 3<x<4$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 04 Aug 2010 Posts: 477 Schools: Dartmouth College Re: Which of the following is the solution set for the inequality 0<|x|-2x [#permalink] ### Show Tags 28 Mar 2019, 04:08 MathRevolution 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. . _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Intern Joined: 26 Feb 2017 Posts: 6 Re: Which of the following is the solution set for the inequality 0<|x|-2x [#permalink] ### Show Tags 31 Mar 2019, 14:08 When solving the absolute value inequality after x I got: 0>x>-3 0>x>-1 Manager Joined: 21 Feb 2019 Posts: 125 Location: Italy Re: Which of the following is the solution set for the inequality 0<|x|-2x [#permalink] ### Show Tags 31 Mar 2019, 14:39 2 $$0 < |x| -2x < 3$$ Case A: $$x ≥ 0$$ $$0 < -x < 3$$ $$-3 < x< 0$$ There are no solutions here since $$x ≥ 0$$. Case B: $$x < 0$$ $$0 < -3x < 3$$ $$0 < -x < 1$$ $$-1 < x < 0$$ That's what we were looking for. Hence, $$A$$. _________________ If you like my post, Kudos are appreciated! Thank you. MEMENTO AUDERE SEMPER Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8024 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is the solution set for the inequality 0<|x|-2x [#permalink] ### Show Tags 31 Mar 2019, 18:34 1 => By definition, if $$x ≥ 0$$, then $$|x| = x$$ and if $$x < 0, |x| = -x.$$ If $$x ≥ 0$$, 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 $$x ≥ 0$$. 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 $$-1<x<0.$$ Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Which of the following is the solution set for the inequality 0<|x|-2x   [#permalink] 31 Mar 2019, 18:34
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