We are solving the inequality:

$-9 - 3x \leq 9$

Step 1: Simplify the inequality

Add $9$ to both sides to eliminate the constant on the left-hand side: $-9 - 3x + 9 \leq 9 + 9$ $-3x \leq 18$

Step 2: Solve for $x$

Divide both sides by $-3$. Remember, dividing by a negative number reverses the inequality: $x \geq \frac{18}{-3}$ $x \geq -6$

Final Answer:

$x \geq -6$

Would you like a graph of the solution or further clarification? 😊

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Related Questions:

1. How do you graph the solution $x \geq -6$ on a number line?
2. What happens when you divide by a negative number in an inequality?
3. Can you turn this inequality into an equivalent equation? If so, how?
4. How do you verify a solution to an inequality?
5. How do inequalities relate to systems of inequalities in two variables?

Tip:

Always double-check inequality direction changes when multiplying or dividing by a negative number!