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 \(D\)

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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.