To solve the inequality [tex]\(5x - 9 \leq 21\)[/tex], follow these steps:
1. Isolate the variable term:
- Start by eliminating the constant term on the left side. To do this, add 9 to both sides of the inequality:
[tex]\[
5x - 9 + 9 \leq 21 + 9
\][/tex]
which simplifies to:
[tex]\[
5x \leq 30
\][/tex]
2. Solve for the variable:
- Now, divide both sides of the inequality by 5 to isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{5x}{5} \leq \frac{30}{5}
\][/tex]
which simplifies to:
[tex]\[
x \leq 6
\][/tex]
Hence, the solution set for the inequality [tex]\(5x - 9 \leq 21\)[/tex] is:
[tex]\[
x \leq 6
\][/tex]
Among the given options, the correct answer is:
[tex]\[
x \leq 6
\][/tex]
