Sure, let's solve the inequality step by step:
The inequality we need to solve is:
[tex]\[
-\frac{x}{4} > 8
\][/tex]
Step 1: The first step is to eliminate the fraction by multiplying both sides of the inequality by [tex]\( -4 \)[/tex]. Remember, when we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign.
So, we multiply both sides by [tex]\(-4\)[/tex]:
[tex]\[
-\frac{x}{4} \times (-4) < 8 \times (-4)
\][/tex]
Step 2: Simplify both sides of the inequality.
[tex]\[
x < -32
\][/tex]
Thus, the solution to the inequality [tex]\(-\frac{x}{4} > 8\)[/tex] is [tex]\(x < -32\)[/tex].
The correct answer is:
D. [tex]\(x < -32\)[/tex]
