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QOTD#25 |1 – 5| = |5 – m|
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28 Sep 2016, 14:45
28 Sep 2016, 14:45
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Question Stats:
73% (00:38) correct
26% (00:45) wrong based on 180 sessions
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\(|1 - 5| = |5 - m|\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
m |
4 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Drill 1
Question: 3
Page: 282
Question: 3
Page: 282
Re: QOTD#25 |1 – 5| = |5 – m|
[#permalink]
28 Sep 2016, 14:47
28 Sep 2016, 14:47
3
Expert Reply
Explanation
We solve for m.
If \(|1 - 5| = |5 - m|\), then \(|- 4| = |5 - m|\), or \(4 = |5 - m|\).
When you see absolute values, remember to consider both positive and negative solutions: \(5 - m = 4\) or \(5 - m = -4\), so m can equal 1 or 9, leaving you with choice D for the answer.
We solve for m.
If \(|1 - 5| = |5 - m|\), then \(|- 4| = |5 - m|\), or \(4 = |5 - m|\).
When you see absolute values, remember to consider both positive and negative solutions: \(5 - m = 4\) or \(5 - m = -4\), so m can equal 1 or 9, leaving you with choice D for the answer.
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Re: QOTD#25 |1 – 5| = |5 – m|
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12 Nov 2016, 06:50
12 Nov 2016, 06:50
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sandy wrote:
\(|1 - 5| = |5 - m|\)
Quantity A |
Quantity B |
m |
4 |
When solving equations involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
So, if |1 - 5| = |5 - m|, then we must consider two cases:
1 - 5 = 5 - m and 1 - 5 = -(5 - m)
1 - 5 = 5 - m
-4 = 5 - m
-9 = -m
m = 9
[b]1 - 5 = -(5 - m)
-4 = -5 + m
1 = m
So, we have two solutions: m = 9 and m = 1
Now plug them into the original equation to ensure they work.
m = 9
|1 - 5| = |5 - 9|
|-4| = |-4|
4 = 4
WORkS!
m = 1
|1 - 5| = |5 - 1|
|-4| = |4|
4 = 4
WORKS!
If m = 9, then Quantity A is greater
If m = 1, then Quantity B is greater
Answer:
Show: ::
D
