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Which of the following inequalities represents the entire solution set

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

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New post 15 Apr 2018, 10:01
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A
B
C
D
E

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82% (00:42) correct 18% (00:18) wrong based on 22 sessions

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

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New post 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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Re: Which of the following inequalities represents the entire solution set [#permalink]

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New post 15 Apr 2018, 14:10
Answer is D

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   [#permalink] 15 Apr 2018, 14:10
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Which of the following inequalities represents the entire solution set

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