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If |x/4| > 1 which of the following must be true?
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16 Apr 2018, 10:00
16 Apr 2018, 10:00
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66% (00:20) correct
33% (00:49) wrong based on 27 sessions
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If \(|\frac{x}{4}| > 1\), which of the following must be true?
A. \(x > 4\)
B. \(x < 4\)
C. \(x = 4\)
D. \(x \neq 4\)
E. \(x < - 4\)
A. \(x > 4\)
B. \(x < 4\)
C. \(x = 4\)
D. \(x \neq 4\)
E. \(x < - 4\)
Re: If |x/4| > 1 which of the following must be true?
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18 Apr 2018, 01:29
18 Apr 2018, 01:29
1
since the inequality involves modulus we should account for both +ve and -ve value
For\(+\)ve value
\(x/4 > 1\)
therefore, \(x>4\)
For \(-\)ve value
\(x/4 < -1\) (Since this is a inequality multiplying by \(-\)ve number flips the inequality symbol)
\(x < -4\)
The correct option should satisfy both the situation and only choice D does that when x is not equal to \(4\)
For\(+\)ve value
\(x/4 > 1\)
therefore, \(x>4\)
For \(-\)ve value
\(x/4 < -1\) (Since this is a inequality multiplying by \(-\)ve number flips the inequality symbol)
\(x < -4\)
The correct option should satisfy both the situation and only choice D does that when x is not equal to \(4\)
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If |x/4| > 1 which of the following must be true?
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31 Dec 2021, 01:58
31 Dec 2021, 01:58
1
Given that \(\mid \frac{x}{4} \mid > 1\) and we need to find the range of values of x
\(\mid \frac{x}{4} \mid > 1\) can be written as \(\frac{\mid x \mid }{\mid 4 \mid } > 1\)
And we know that | 4 | = 4 as 4 is a positive number
=> \(\frac{\mid x \mid }{ 4} > 1\)
=> | x | > 4
Now, this is of the form | x | > a and we know that we can open it as
Either x > a or x < -a
=> x > 4 or x < -4
=> x \(\neq\) 4
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
\(\mid \frac{x}{4} \mid > 1\) can be written as \(\frac{\mid x \mid }{\mid 4 \mid } > 1\)
And we know that | 4 | = 4 as 4 is a positive number
=> \(\frac{\mid x \mid }{ 4} > 1\)
=> | x | > 4
Now, this is of the form | x | > a and we know that we can open it as
Either x > a or x < -a
=> x > 4 or x < -4
=> x \(\neq\) 4
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
