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# Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0

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Math Revolution GMAT Instructor
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Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

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04 Oct 2017, 00:45
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Difficulty:

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Question Stats:

50% (01:56) correct 50% (02:00) wrong based on 278 sessions

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[GMAT math practice question]

Which of the following inequalities is equal to |2x-|x||<6?

A. -2<x<0
B. 0<x<6
C. -2<x<6
D. -2<x<2
E. -6<x<6

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Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

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04 Oct 2017, 01:31
4
3
MathRevolution wrote:
[GMAT math practice question]

Which of the following inequalities is equal to |2x-|x||<6?

A. -2<x<0
B. 0<x<6
C. -2<x<6
D. -2<x<2
E. -6<x<6

You can write the inequality as:

-6 < |2x-|x|| < 6

Case 1:
If x >= 0 ; |x| = x
|2x-|x|| becomes 2x - x = x

-6 < x < 6
But as x>=0 we only take the values as 0 < x < 6

Case 2:
If x < 0 ; |x| = -x
|2x-|x|| becomes 2x + x = 3x

-6 < 3x < 6
-2 < x < 2
But as x < 0 we only take the values as -2 < x < 0

Combining the results of Case 1 and 2
-2 < x < 6
##### General Discussion
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Posts: 64250
Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

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04 Oct 2017, 00:47
2
MathRevolution wrote:
[GMAT math practice question]

Which of the following inequalities is equal to |2x-|x||<6?

A. -2<x<0
B. 0<x<6
C. -2<x<6
D. -2<x<2
E. -6<x<6

Similar question: https://gmatclub.com/forum/which-of-the ... 47913.html
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Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

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04 Oct 2017, 02:44
the maximum range provided in the answer is -6, -2, 2, 0 and 6
check for this range

-6, gives us that |-12-|-6||<6
|-12-6| <6
18<6 not true
Eliminate E

next value given in the answer series is -2
Holds good, so left value in the number line should be 2

Now check for right value by putting 6
Holds good so the range should be -2 to 6

So clearly answer should be C
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

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06 Oct 2017, 01:42
=>

We should split real number of x into two cases x ≥ 0 and x < 0.

Case 1: x ≥ 0
|2x-|x||<6 ⬄ | 2x – x | < 6 ⬄ |x| < 6 ⬄ -6<x<6.
From the assumption of the case, x ≥ 0, we have 0 ≤ x < 6.

Case 2: x < 0
|2x-|x||<6 ⬄ | 2x + x | < 6 ⬄ |3x| < 6 ⬄ |x| < 2 ⬄ -2<x<2.
From the assumption of the case, x < 0, we have -2<x<0.

Thus, we have -2 < x < 6.

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Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

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09 Feb 2019, 03:24
Bunuel - Can you help me understand where did I go wrong?
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Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0   [#permalink] 09 Feb 2019, 03:24