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16 Sep 2014, 01:08
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A
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Difficulty:
35%
(medium)
Question Stats:
67% (01:05) correct
33%
(01:15)
wrong
based on 449
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If set \(S\) contains all distinct solutions of the equation \(|x - 4| = x\), what is the range of set \(S\)?
A. 0
B. 2
C. 4
D. 6
E. 8
A. 0
B. 2
C. 4
D. 6
E. 8
16 Sep 2014, 01:08
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Official Solution:
If set \(S\) contains all distinct solutions of the equation \(|x - 4| = x\), what is the range of set \(S\)?
A. 0
B. 2
C. 4
D. 6
E. 8
If \(x\) is greater than or equal to 4, the equation \(|x - 4| = x\) becomes \(x - 4 = x\). This equation has no solutions.
If \(x\) is less than 4, the equation \(|x - 4| = x\) transforms into \(4 - x = x\), which yields \(x = 2\).
Therefore, set \(S\) has only one element: 2. The range of any single-element set is 0.
Answer: A
If set \(S\) contains all distinct solutions of the equation \(|x - 4| = x\), what is the range of set \(S\)?
A. 0
B. 2
C. 4
D. 6
E. 8
If \(x\) is greater than or equal to 4, the equation \(|x - 4| = x\) becomes \(x - 4 = x\). This equation has no solutions.
If \(x\) is less than 4, the equation \(|x - 4| = x\) transforms into \(4 - x = x\), which yields \(x = 2\).
Therefore, set \(S\) has only one element: 2. The range of any single-element set is 0.
Answer: A
General Discussion
12 Oct 2017, 06:14
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Bunuel
Point noted.
simple logic. But would have costed more on the exam
Thankfully, I learned it now itself
