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. \(x < -4\)
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 < -kNote: these rules assume that k is positive
GIVEN: |x/4| > 1From 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 < -4So, the only answer choice that MUST be true is D.
Cheers,
Brent