To solve the inequality [tex]\(\frac{x}{3} \leq -6\)[/tex], we need to isolate the variable [tex]\(x\)[/tex]. Here are the detailed steps:
1. Start with the given inequality:
[tex]\[
\frac{x}{3} \leq -6
\][/tex]
2. To clear the fraction, we multiply both sides of the inequality by 3. This helps to isolate [tex]\(x\)[/tex]. Remember, multiplying or dividing both sides of an inequality by a positive number does not change the direction of the inequality:
[tex]\[
3 \cdot \frac{x}{3} \leq 3 \cdot (-6)
\][/tex]
3. Simplify the left-hand side by multiplying:
[tex]\[
x \leq -18
\][/tex]
Thus, the solution to the inequality [tex]\(\frac{x}{3} \leq -6\)[/tex] is:
[tex]\[
x \leq -18
\][/tex]
Among the given choices, the correct one is:
[tex]\[
x \leq -18
\][/tex]
