What is the solution to the following inequality?

[tex]\[
\frac{x}{-3} \leq 3
\][/tex]

A. [tex]\( x \geq 6 \)[/tex]

B. [tex]\( x \geq 1 \)[/tex]

C. [tex]\( x \leq -9 \)[/tex]

D. [tex]\( x \geq -9 \)[/tex]



Answer :

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].