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Which of the following inequalities is equivalent to |2x-|x||<3?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Which of the following inequalities is equivalent to |2x-|x||<3?  [#permalink]

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28 Mar 2018, 02:03
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[GMAT math practice question]

Which of the following inequalities is equivalent to $$|2x-|x||<3$$?

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

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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" Most Helpful Expert Reply Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following inequalities is equivalent to |2x-|x||<3? [#permalink] Show Tags 30 Mar 2018, 02:07 2 5 => $$|2x-|x||<3$$ $$=> -3 < 2x – |x| < 3$$ Case 1: If $$x ≥ 0$$, then $$|x| = x$$, and so $$-3 < 2x – |x| < 3$$ $$=> -3 < x < 3$$ $$=> 0 ≤ x < 3$$, since $$x ≥ 0$$. Case 2: If $$x < 0$$, then $$|x| = - x$$, and so $$-3 < 2x – |x| < 3$$ $$=> -3 < 3x < 3$$ $$=> - 1< x < 1$$ $$=> - 1< x < 0$$, since $$x < 0$$. Thus,$$-1 < x < 3$$. Therefore, the answer is C. Answer: C _________________ 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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Joined: 20 Feb 2017
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Location: India
Concentration: Operations, Strategy
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Re: Which of the following inequalities is equivalent to |2x-|x||<3?  [#permalink]

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28 Mar 2018, 02:38
2
squaring both sides
4x^2+X^2-4x|x|<9
5x^2-4x|x|<9
if x>0
x^2<9
this means 0<x<3 --------1
if x<0
x^2<1
this means -1<x<0 -------------2
combining 1 and 2
-1<x<3 option C
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Joined: 10 Jun 2019
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Re: Which of the following inequalities is equivalent to |2x-|x||<3?  [#permalink]

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20 Jun 2019, 21:21
On evaluating the outermost modulus, we get -3 < 2x - |x| < 3.
Now, we have 2 conditions, when x >= 0, we get -3 < x < 3. But x cannot be less than 0, so 0 <= x < 3.
When x < 0, we get -3 < 3x < 3. This gives us -1 < x < 1. But x has to be lesser than 0, so -1 < x < 0.
From the above two ranges for x, we can say -1 < x < 3. Hence, Option C is the right choice.
Re: Which of the following inequalities is equivalent to |2x-|x||<3?   [#permalink] 20 Jun 2019, 21:21
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