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

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Math Revolution GMAT Instructor
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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
1
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

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

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New post 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.
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Re: Which of the following inequalities is equivalent to |2x-|x||<3?   [#permalink] 20 Jun 2019, 21:21
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Which of the following inequalities is equivalent to |2x-|x||<3?

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