To solve the inequality [tex]\(-8x \leq 2\)[/tex], we will follow these steps:
1. Isolate [tex]\( x \)[/tex]: The goal is to get [tex]\( x \)[/tex] by itself on one side of the inequality. To isolate [tex]\( x \)[/tex], divide both sides of the inequality by [tex]\(-8\)[/tex]. Note that when you divide by a negative number, the direction of the inequality sign reverses.
2. Step-by-step isolation:
[tex]\[
-8x \leq 2
\][/tex]
Divide both sides by [tex]\(-8\)[/tex]:
[tex]\[
x \geq \frac{2}{-8}
\][/tex]
3. Simplify the fraction:
[tex]\[
\frac{2}{-8} = -0.25
\][/tex]
Thus, we get:
[tex]\[
x \geq -0.25
\][/tex]
Therefore, the solution to the inequality [tex]\(-8x \leq 2\)[/tex] is:
[tex]\[
x \geq -0.25
\][/tex]
Comparing this with the given options, the correct answer is:
D) [tex]\( x \geq -0.25 \)[/tex]
