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21 Apr 2024, 10:52
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E
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Difficulty:
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Question Stats:
78% (00:42) correct
22%
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based on 9
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If \(|a - b| = |b - c| = 2\) and \(a < b < c\), what is the value of \(|a - c|\)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
21 Apr 2024, 10:52
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Official Solution:
If \(|a - b| = |b - c| = 2\) and \(a < b < c\), what is the value of \(|a - c|\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given that \(a < b\), we can deduce that \(|a-b| = -(a-b) = 2\), which simplifies to \(b-a = 2\). Similarly, since \(b < c\) is given, we can deduce that \(|b-c| = -(b-c) = 2\), which simplifies to \(c-b = 2\). By adding these two equations: \((b-a) + (c-b) = 2 + 2\), we get \(c-a = 4\). Therefore, \(|a-c| = 4\).
Answer: E
If \(|a - b| = |b - c| = 2\) and \(a < b < c\), what is the value of \(|a - c|\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given that \(a < b\), we can deduce that \(|a-b| = -(a-b) = 2\), which simplifies to \(b-a = 2\). Similarly, since \(b < c\) is given, we can deduce that \(|b-c| = -(b-c) = 2\), which simplifies to \(c-b = 2\). By adding these two equations: \((b-a) + (c-b) = 2 + 2\), we get \(c-a = 4\). Therefore, \(|a-c| = 4\).
Answer: E
21 Sep 2024, 15:56
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The distance from a to b is 2 and the distance from b to c is 2 so the distance from a to c will 2+ 2 = 4.
Is it the correct way to do?
Is it the correct way to do?
