To solve the inequality [tex]\(-8x \leq 2\)[/tex], follow these steps:
1. Isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to divide both sides of the inequality by [tex]\(-8\)[/tex].
2. Important Note on Inequality:
Dividing both sides of an inequality by a negative number reverses the direction of the inequality sign. Therefore, when we divide by [tex]\(-8\)[/tex], the [tex]\(\leq\)[/tex] sign will become a [tex]\(\geq\)[/tex] sign.
3. Perform the Division:
[tex]\[
-8x \leq 2 \implies x \geq \frac{2}{-8}
\][/tex]
4. Simplify the Fraction:
Simplify [tex]\(\frac{2}{-8}\)[/tex]:
[tex]\[
\frac{2}{-8} = -0.25
\][/tex]
Thus, the solution to the inequality [tex]\(-8x \leq 2\)[/tex] is:
[tex]\[
x \geq -0.25
\][/tex]
Given the options:
A. [tex]\(x \geq -25\)[/tex]
B. [tex]\(x \leq 25\)[/tex]
C. [tex]\(x \leq -25\)[/tex]
D. [tex]\(x \geq -30\)[/tex]
The best answer is not explicitly listed in the choices. The correct inequality [tex]\(x \geq -0.25\)[/tex] does not align with most of the significant figures provided in the options. However, if we prioritize comparing magnitudes, none of these options correctly correspond to the exact calculated answer.
Please verify if the options contain a typographic error or consider providing a different set of choices that include [tex]\(x \geq -0.25\)[/tex].
