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04 Sep 2020, 20:00
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Difficulty:
45%
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Question Stats:
68% (01:56) correct
32%
(02:12)
wrong
based on 1603
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What is the median of all the values of x, which satisfy \(||x – 3| – 5| = 3\) ?
A. 1
B. 2
C. 3
D. 5
E. 6
M37-85
A. 1
B. 2
C. 3
D. 5
E. 6
|
M37-85
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03 Dec 2021, 02:39
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Official Solution:
What is the median of all the values of \(x\), which satisfy \(||x – 3| – 5| = 3\) ?
A. \(1\)
B. \(2\)
C. \(3\)
D. \(5\)
E. \(6\)
\(||x – 3| – 5| = 3\) means that \(|x – 3| – 5 = 3\) or \(|x – 3| – 5 = -3\).
CASE 1:
\(|x – 3| – 5 = 3\);
\(|x – 3| = 8\);
\(x=11\) or \(x=-5\)
CASE 2:
\(|x – 3| – 5 = -3\);
\(|x – 3| = 2\);
\(x=5\) or \(x=1\)
So, \(x\) can be (in ascending order): -5, 1, 5, or 11. The median of the values is \(\frac{1+5}{2}=3\).
Answer: C
What is the median of all the values of \(x\), which satisfy \(||x – 3| – 5| = 3\) ?
A. \(1\)
B. \(2\)
C. \(3\)
D. \(5\)
E. \(6\)
\(||x – 3| – 5| = 3\) means that \(|x – 3| – 5 = 3\) or \(|x – 3| – 5 = -3\).
CASE 1:
\(|x – 3| – 5 = 3\);
\(|x – 3| = 8\);
\(x=11\) or \(x=-5\)
CASE 2:
\(|x – 3| – 5 = -3\);
\(|x – 3| = 2\);
\(x=5\) or \(x=1\)
So, \(x\) can be (in ascending order): -5, 1, 5, or 11. The median of the values is \(\frac{1+5}{2}=3\).
Answer: C
General Discussion
04 Sep 2020, 20:07
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What is the median of all the values of x, which satisfy ?
||X -3|-5| = 3
|X-3-5|=3
|X -8| = 3
-3 = x -8 = 3
5 = x = 11
Now, |-x + 3 -5| = 3
-3 = -x -2 = 3
-1 = -x = 5
1 = x = -5
The four values of x are : -5, 1, 5, 11
Median is 3.
A. 1
B. 2
C. 3
D. 5
E. 6
C is the answer.
Posted from my mobile device
||X -3|-5| = 3
|X-3-5|=3
|X -8| = 3
-3 = x -8 = 3
5 = x = 11
Now, |-x + 3 -5| = 3
-3 = -x -2 = 3
-1 = -x = 5
1 = x = -5
The four values of x are : -5, 1, 5, 11
Median is 3.
A. 1
B. 2
C. 3
D. 5
E. 6
C is the answer.
Posted from my mobile device
