To solve the inequality [tex]\(\frac{x}{-3} \leq 3\)[/tex], we need to isolate [tex]\(x\)[/tex]. Here is the step-by-step process:
1. Start with the given inequality:
[tex]\[
\frac{x}{-3} \leq 3
\][/tex]
2. To clear the fraction, we multiply both sides of the inequality by [tex]\(-3\)[/tex].
Note: When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign reverses.
Doing this, we get:
[tex]\[
x \geq 3 \times (-3)
\][/tex]
3. Calculate the right-hand side:
[tex]\[
3 \times (-3) = -9
\][/tex]
4. Therefore, the inequality becomes:
[tex]\[
x \geq -9
\][/tex]
Thus, the solution to the inequality [tex]\(\frac{x}{-3} \leq 3\)[/tex] is:
[tex]\[
x \geq -9
\][/tex]
So, the correct answer is:
C. [tex]\(x \geq -9\)[/tex]
