To solve the inequality [tex]\(-8x + 4 \leq 36\)[/tex], follow these step-by-step instructions:
1. Isolate the variable term: Start by moving the constant term to the right side of the inequality. We do this by subtracting 4 from both sides:
[tex]\[
-8x + 4 - 4 \leq 36 - 4
\][/tex]
Simplifying, we get:
[tex]\[
-8x \leq 32
\][/tex]
2. Solve for [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], we need to divide both sides of the inequality by [tex]\(-8\)[/tex]. Remember, dividing by a negative number reverses the inequality sign:
[tex]\[
x \geq \frac{32}{-8}
\][/tex]
Simplifying the fraction:
[tex]\[
x \geq -4
\][/tex]
3. Compare with provided options:
A. [tex]\(x \leq -4\)[/tex]
B. [tex]\(x \leq 4\)[/tex]
C. [tex]\(x \geq 4\)[/tex]
D. [tex]\(x \geq -4\)[/tex]
The correct answer is:
[tex]\[
\boxed{D. \ x \geq -4}
\][/tex]
