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

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

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New post 28 Mar 2019, 01:42
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A
B
C
D
E

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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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Re: Which of the following is the solution set for the inequality 0<|x|-2x  [#permalink]

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New post 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.

.
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Re: Which of the following is the solution set for the inequality 0<|x|-2x  [#permalink]

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New post 31 Mar 2019, 14:08
When solving the absolute value inequality after x I got:

0>x>-3
0>x>-1
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Re: Which of the following is the solution set for the inequality 0<|x|-2x  [#permalink]

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New post 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, \(A\).
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Re: Which of the following is the solution set for the inequality 0<|x|-2x  [#permalink]

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New post 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
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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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