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

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Which of the following inequalities is equivalent to |2x-|x||<3? [#permalink]

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

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

\(A. 0<x<2\)
\(B. 0<x<3\)
\(C. -1<x<3\)
\(D. 0<x<1\)
\(E. -3<x<1\)
[Reveal] Spoiler: OA

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Re: Which of the following inequalities is equivalent to |2x-|x||<3? [#permalink]

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New post 28 Mar 2018, 02:38
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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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Re: Which of the following inequalities is equivalent to |2x-|x||<3? [#permalink]

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New post 30 Mar 2018, 02:07
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=>

\(|2x-|x||<3\)
\(=> -3 < 2x – |x| < 3\)

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
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Re: Which of the following inequalities is equivalent to |2x-|x||<3?   [#permalink] 30 Mar 2018, 02:07
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Which of the following inequalities is equivalent to |2x-|x||<3?

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