1. **State the problem:** Solve the inequality $$-6x - 3 \geq 9$$ and graph the solution on a number line. 2. **Write the inequality:** $$-6x - 3 \geq 9$$ 3. **Add 3 to both sides to isolate the term with $x$:** $$-6x - 3 + 3 \geq 9 + 3$$ $$-6x \geq 12$$ 4. **Divide both sides by $-6$ to solve for $x$.** Remember, dividing by a negative number reverses the inequality sign: $$x \leq \frac{12}{-6}$$ 5. **Simplify the fraction:** $$x \leq \cancel{\frac{12}{-6}} = -2$$ 6. **Final solution:** $$x \leq -2$$ 7. **Interpretation:** The solution means $x$ can be any number less than or equal to $-2$. 8. **Graph description:** On the number line, shade all values to the left of $-2$ including $-2$ itself (closed circle at $-2$).