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19 Nov 2021, 04:46
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What is the range of the roots of \(||x – 1| – 2| = 1\)?
A. \(0\)
B. \(2\)
C. \(4\)
D. \(6\)
E. \(8\)
A. \(0\)
B. \(2\)
C. \(4\)
D. \(6\)
E. \(8\)
19 Nov 2021, 04:46
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Official Solution:
What is the range of the roots of \(||x – 1| – 2| = 1\)?
A. \(0\)
B. \(2\)
C. \(4\)
D. \(6\)
E. \(8\)
\(||x – 1| – 2| = 1\)
\(|x – 1| – 2 = 1\) or \(||x – 1| – 2| = -1\)
CASE 1:
\(|x – 1| – 2 = 1\)
\(|x – 1| = 3\)
\(x=4\) or \(x=-2\).
CASE 2:
\(|x – 1| – 2 = -1\)
\(|x – 1| = 1\)
\(x=2\) or \(x=0\).
So, \(x\) can be -2, 0, 2, and 4. The range of values \(= 4-(-2)=6\).
Answer: D
What is the range of the roots of \(||x – 1| – 2| = 1\)?
A. \(0\)
B. \(2\)
C. \(4\)
D. \(6\)
E. \(8\)
\(||x – 1| – 2| = 1\)
\(|x – 1| – 2 = 1\) or \(||x – 1| – 2| = -1\)
CASE 1:
\(|x – 1| – 2 = 1\)
\(|x – 1| = 3\)
\(x=4\) or \(x=-2\).
CASE 2:
\(|x – 1| – 2 = -1\)
\(|x – 1| = 1\)
\(x=2\) or \(x=0\).
So, \(x\) can be -2, 0, 2, and 4. The range of values \(= 4-(-2)=6\).
Answer: D
BatrickPatemann
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09 Jan 2025, 15:55
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I like the solution - it’s helpful.
