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# Which of the following inequalities represents the entire solution set

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Math Expert
Joined: 02 Sep 2009
Posts: 47183
Which of the following inequalities represents the entire solution set  [#permalink]

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15 Apr 2018, 10:01
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Difficulty:

25% (medium)

Question Stats:

76% (00:37) correct 24% (00:50) wrong based on 58 sessions

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Which of the following inequalities represents the entire solution set for x if |x| > x?

A. x ≥ 0
B. x > 0
C. x ≤ 0
D. x < 0
E. x < −1

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Which of the following inequalities represents the entire solution set  [#permalink]

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15 Apr 2018, 11:47
Bunuel wrote:
Which of the following inequalities represents the entire solution set for x if |x| > x?

A. x ≥ 0
B. x > 0
C. x ≤ 0
D. x < 0
E. x < −1

$$|x|<x$$, is only possible when $$x<0$$

Option $$D$$

------------------------------------

Algebraically, we can have two cases -

Case 1: if $$x≥0$$, then $$|x|=x$$,

so equation will become $$x>x$$, or $$0>0$$ which is not possible. Hence discard Case 1.

Case 2: if $$x<0$$, then $$|x|=-x$$

so equation will become $$-x>x$$, or $$0>2x=>x<0$$ which is True in this case.
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Joined: 08 Sep 2016
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Re: Which of the following inequalities represents the entire solution set  [#permalink]

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15 Apr 2018, 14:10

The reason why it can't be C is that |x| means values that are nonnegative, so positive numbers and 0 are valid. |0|>0 is not true hence not correct.
Re: Which of the following inequalities represents the entire solution set &nbs [#permalink] 15 Apr 2018, 14:10
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