To solve the inequality [tex]\(-24 \leq x - 3 - 8x\)[/tex], we follow a step-by-step process:
1. Simplify the inequality:
[tex]\[
-24 \leq x - 3 - 8x
\][/tex]
2. Combine like terms on the right-hand side:
[tex]\[
-24 \leq x - 8x - 3
\][/tex]
Simplifying further:
[tex]\[
-24 \leq -7x - 3
\][/tex]
3. Isolate the term with [tex]\(x\)[/tex]:
Add 3 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-24 + 3 \leq -7x
\][/tex]
Simplifying this, we get:
[tex]\[
-21 \leq -7x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by [tex]\(-7\)[/tex]. Remember that dividing by a negative number reverses the inequality sign:
[tex]\[
\frac{-21}{-7} \geq x
\][/tex]
Simplifying the left-hand side:
[tex]\[
3 \geq x
\][/tex]
Which can be rewritten as:
[tex]\[
x \leq 3
\][/tex]
The solution to the inequality is [tex]\(x \leq 3\)[/tex]. Thus, the best answer is:
D. [tex]\(x \leq 3\)[/tex]
