To solve the inequality [tex]\( 5x - 9 \leq 21 \)[/tex], let's follow the steps systematically:
1. Start with the given inequality:
[tex]\( 5x - 9 \leq 21 \)[/tex]
2. Add 9 to both sides of the inequality to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
5x - 9 + 9 \leq 21 + 9
\][/tex]
Simplifying this results in:
[tex]\[
5x \leq 30
\][/tex]
3. Divide both sides of the inequality by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{5x}{5} \leq \frac{30}{5}
\][/tex]
Simplifying this gives:
[tex]\[
x \leq 6
\][/tex]
So, the solution set of the inequality [tex]\( 5x - 9 \leq 21 \)[/tex] is:
[tex]\[
x \leq 6
\][/tex]
Hence, the correct answer is [tex]\( \boxed{x \leq 6} \)[/tex].
