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Which of the following is the solution set for the inequalit

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by Max@Math Revolution » Thu Mar 28, 2019 12:36 am
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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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by GMATGuruNY » Thu Mar 28, 2019 3:06 am
Max@Math Revolution 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.

The correct answer is A.
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by Max@Math Revolution » Sun Mar 31, 2019 5:27 pm
=>

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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