To solve the inequality [tex]\(5x - 9 \leq 21\)[/tex], let's follow these step-by-step instructions:
1. Start with the given inequality:
[tex]\[
5x - 9 \leq 21
\][/tex]
2. Isolate the term with the variable [tex]\( x \)[/tex]:
First, add 9 to both sides of the inequality to get rid of the constant term on the left side:
[tex]\[
5x - 9 + 9 \leq 21 + 9
\][/tex]
Simplifying, we obtain:
[tex]\[
5x \leq 30
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Next, divide both sides of the inequality by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{5x}{5} \leq \frac{30}{5}
\][/tex]
This simplifies to:
[tex]\[
x \leq 6
\][/tex]
Therefore, the solution set of the inequality [tex]\(5x - 9 \leq 21\)[/tex] is:
[tex]\[
x \leq 6
\][/tex]
To summarize, the correct representation of the solution set is:
[tex]\[
x \leq 6
\][/tex]
So, the answer is:
[tex]\[
\boxed{x \leq 6}
\][/tex]
