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

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

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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
[Reveal] Spoiler: OA

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

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New post 04 Oct 2017, 02:31
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
Answer : C

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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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New post 04 Oct 2017, 03:44
1. check the answers
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
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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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New post 06 Oct 2017, 02:42
=>

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.

Answer: C
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Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0   [#permalink] 06 Oct 2017, 02:42
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