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15 Apr 2018, 10:01
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D
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Difficulty:
15%
(low)
Question Stats:
78% (00:48) correct
22%
(00:58)
wrong
based on 297
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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
A. x ≥ 0
B. x > 0
C. x ≤ 0
D. x < 0
E. x < −1
15 Apr 2018, 11:47
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Bunuel
\(|x|<x\), 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.
15 Apr 2018, 14:10
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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.
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.
