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