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07 May 2020, 09:09
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:30) correct
33%
(01:40)
wrong
based on 1168
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What is the minimum value of |x +11| - |x - 7|?
A. -18
B. -4
C. 0
D. 4
E. 18
A. -18
B. -4
C. 0
D. 4
E. 18
@Experts how is the answer -18? if i take x = -11 |-11+11| - |-11-7| => - |-18| => value inside the mod is <0 therefore -18 will come out when i remove the mod -(-18) = +18
could someone correct what im doing wrong?
could someone correct what im doing wrong?
07 May 2020, 09:30
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Kritisood
Critical points of |x +11| - |x - 7| are -11 and 7.
When \(x < -11\), then \(x + 11 < 0\) and \(x - 7 < 0\), which means that for this range \(|x +11| = -(x + 11)\) and \(|x - 7| = -(x - 7) = 7 - x\). So, in this range \(|x +11| - |x - 7| = -(x + 11) - (7 - x) = -18\).
When \(-11 \leq x \leq 7,\) then \(x + 11 \geq 0\) and \(x - 7 \leq 0\), which means that for this range \(|x +11| = x + 11\) and \(|x - 7| = -(x - 7) = 7 - x\). So, in this range \(|x +11| - |x - 7| = x + 11 - (7 - x) = 2x + 4\). The least value for \(2x + 4\) for given range is when \(x = -11\), so the lowest value is -18.
When \(x > 7\), then \(x + 11 > 0\) and \(x - 7 > 0\), which means that for this range \(|x +11| = x + 11\) and \(|x - 7| = x - 7\). So, in this range \(|x +11| - |x - 7| = x + 11) - (x - 7) = 18\).
Answer: A.
The graph of |x +11| - |x - 7| is given below:
Quote:
If \(x = -11\), \(|x +11| - |x - 7| = |-11 +11| - |-11 - 7| = |0| - |-18| = 0 - 18 = -18\). (|-18| is 18)
The way you are doing: \(- |-18| = -(-(-18)) = -18\).
Attachment:
Untitled.png [ 5.12 KiB | Viewed 15921 times ]
29 Sep 2020, 23:31
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[X + 11] - [X - 7] = ?
We MINIMIZE the Value of this Expression when:
(1)we pick an X such that the effect of [X + 11] is MINIMIZED in the Expression
(2)we pick an X such that the effect of - [X - 7] is MAXIMIZED in the Expression
Since the Absolute Value of any Input will ALWAYS be Either 0-Zero or (+)Positive, the LEAST we can make [X + 11] is = 0
this occurs when X = -(11)
Plugging in X = -(11)
[X + 11] - [X - 7] = ?
[-11 + 11] - [-11 -7] =
[0] - [-18] =
0 - 18 = -(18)
-A-
We MINIMIZE the Value of this Expression when:
(1)we pick an X such that the effect of [X + 11] is MINIMIZED in the Expression
(2)we pick an X such that the effect of - [X - 7] is MAXIMIZED in the Expression
Since the Absolute Value of any Input will ALWAYS be Either 0-Zero or (+)Positive, the LEAST we can make [X + 11] is = 0
this occurs when X = -(11)
Plugging in X = -(11)
[X + 11] - [X - 7] = ?
[-11 + 11] - [-11 -7] =
[0] - [-18] =
0 - 18 = -(18)
-A-
