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which of the following must be true?
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10 Mar 2019, 06:43
10 Mar 2019, 06:43
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If \(\mid \frac{x}{4} \mid > 1\) which of the following must be true?
A. \(x > 4\)
B. \(x < 4\)
C. \(x = 4\)
D. \(x ≠ 4\)
E. \(x < -4\)
A. \(x > 4\)
B. \(x < 4\)
C. \(x = 4\)
D. \(x ≠ 4\)
E. \(x < -4\)
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Re: which of the following must be true?
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10 Mar 2019, 08:42
10 Mar 2019, 08:42
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Carcass wrote:
If \(\mid \frac{x}{4} \mid > 1\) which of the following must be true?
A. \(x > 4\)
B. \(x < 4\)
C. \(x = 4\)
D. \(x ≠ 4\)
E. \(x < -4\)
A. \(x > 4\)
B. \(x < 4\)
C. \(x = 4\)
D. \(x ≠ 4\)
E. \(x < -4\)
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
GIVEN: |x/4| > 1
From Rule #2, we can write: EITHER x/4 > 1 OR x/4 < -1
Let's examine each case:
If x/4 > 1, we can multiply both sides by 4 to get: x > 4
If x/4 < -1, we can multiply both sides by 4 to get: x < -4
So, EITHER x > 4 OR x < -4
So, the only answer choice that MUST be true is D.
Cheers,
Brent
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which of the following must be true?
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24 Dec 2021, 09:05
24 Dec 2021, 09:05
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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
Now, lets look at the answer choices
A. \(x > 4\) -> this is partially true it covers only a part of the answer which is x > 4 and does not cover x < -4. So this cannot be "Must be true"
B. \(x < 4\) -> this is NOT TRUE as it contains a lot of numbers which are not in the range. Such as 0
C. \(x = 4\) -> this is NOT TRUE as x is not equal to 4
D. \(x ≠ 4\) -> this is true as x cannot be equal to 4
E. \(x < -4\) -> Same as option A. This is partially true it covers only a part of the answer which is x < -4 and does not cover x > 4. So this cannot be "Must be true"
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
Now, lets look at the answer choices
A. \(x > 4\) -> this is partially true it covers only a part of the answer which is x > 4 and does not cover x < -4. So this cannot be "Must be true"
B. \(x < 4\) -> this is NOT TRUE as it contains a lot of numbers which are not in the range. Such as 0
C. \(x = 4\) -> this is NOT TRUE as x is not equal to 4
D. \(x ≠ 4\) -> this is true as x cannot be equal to 4
E. \(x < -4\) -> Same as option A. This is partially true it covers only a part of the answer which is x < -4 and does not cover x > 4. So this cannot be "Must be true"
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
