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30 Nov 2021, 07:57
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What is the range of all \(x\) satisfying \(|x-2| = x\)?
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
30 Nov 2021, 07:58
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Official Solution:
What is the range of all \(x\) satisfying \(|x-2| = x\)?
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
First of all notice that since \(x\) is equal to an absolute value of some number (\(|x - 2|\)), then \(x\) cannot be negative.
Next, \(|x - 2| = x\) means that either \(x - 2 = x\) or \(-(x - 2) = x\).
The first equation has no solutions for \(x\).
The second equation gives \(x = 1\).
So, \(x\) can only be 1. The range of single element set is 0 (the range \(= {largest} - {smallest} = 1 - 1 = 0\)).
Answer: A
What is the range of all \(x\) satisfying \(|x-2| = x\)?
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
First of all notice that since \(x\) is equal to an absolute value of some number (\(|x - 2|\)), then \(x\) cannot be negative.
Next, \(|x - 2| = x\) means that either \(x - 2 = x\) or \(-(x - 2) = x\).
The first equation has no solutions for \(x\).
The second equation gives \(x = 1\).
So, \(x\) can only be 1. The range of single element set is 0 (the range \(= {largest} - {smallest} = 1 - 1 = 0\)).
Answer: A
15 Aug 2026, 09:51
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I did not quite understand the solution. Does it matter that x = 1 is positive but -(x-2) is negative? Or I dont have to test the value in this case?
