To solve the inequality [tex]\(\frac{x}{-3} \leq 3\)[/tex], follow these steps:
1. Understand the inequality:
The given inequality is [tex]\(\frac{x}{-3} \leq 3\)[/tex]. Our goal is to solve for [tex]\(x\)[/tex].
2. Eliminate the fraction:
To eliminate the fraction, multiply both sides of the inequality by [tex]\(-3\)[/tex].
It's important to remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign must be reversed.
[tex]\[
\frac{x}{-3} \leq 3
\][/tex]
Multiply both sides by [tex]\(-3\)[/tex]:
[tex]\[
x \geq 3 \times -3
\][/tex]
3. Simplify the inequality:
Now simplify the right side:
[tex]\[
x \geq -9
\][/tex]
4. State the solution:
The inequality [tex]\(x \geq -9\)[/tex] represents all [tex]\(x\)[/tex] values that satisfy the given inequality.
So, the correct answer is:
D. [tex]\(x \geq -9\)[/tex].
