To solve the inequality [tex]\(5x - 9 \leq 21\)[/tex], let's go through the steps methodically:
1. Start with the given inequality:
[tex]\[
5x - 9 \leq 21
\][/tex]
2. Isolate the term containing [tex]\(x\)[/tex]:
Add 9 to both sides of the inequality to eliminate the constant term on the left side:
[tex]\[
5x - 9 + 9 \leq 21 + 9
\][/tex]
Simplify this to:
[tex]\[
5x \leq 30
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides of the inequality by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{5x}{5} \leq \frac{30}{5}
\][/tex]
Simplify this to:
[tex]\[
x \leq 6
\][/tex]
Therefore, the solution set for the inequality [tex]\(5x - 9 \leq 21\)[/tex] is:
[tex]\[
x \leq 6
\][/tex]
The correct answer choice is:
[tex]\[
x_1 \leqslant 6
\][/tex]
