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If |x/4| > 1 which of the following must be true?
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15 Jun 2019, 09:40
15 Jun 2019, 09:40
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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 ≠ 4
E. x < -4
A. x > 4
B. x < 4
C. x = 4
D. x ≠ 4
E. x < -4
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Re: If |x/4| > 1 which of the following must be true?
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17 Jun 2019, 05:35
17 Jun 2019, 05:35
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Carcass wrote:
If \(|\frac{x}{4}| > 1\) 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
From rule #2, we can write: EITHER x/4 > 1 OR x/4 < -1
Let's test each case:
Take: x/4 > 1
Multiply both sides by 4 to get: x > 4
Take: x/4 < -1
Multiply both sides by 4 to get: x < -4
IMPORTANT: We're asked to find the answer choice that MUST be true
In our first solution, we get: x > 4
HOWEVER, this does not mean that answer choice A MUST be true, since it could also be the case that x < -4, in which case, answer choice A is NOT true.
So, if we know that EITHER x > 4 OR x < -4, which answer choice MUST be true?
Only answer choice D (x ≠ 4) is true for both possible cases.
Answer: D
Cheers,
Brent
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Re: If |x/4| > 1 which of the following must be true?
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24 Dec 2021, 09:14
24 Dec 2021, 09:14
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
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
