1. **State the problem:** Solve the equation $$-3 = -3| -9 - x |$$. 2. **Isolate the absolute value:** Divide both sides by $$-3$$ to simplify. $$-3 = -3| -9 - x | \implies \cancel{-3} = \cancel{-3}| -9 - x |$$ This simplifies to: $$1 = | -9 - x |$$ 3. **Recall the definition of absolute value:** For any expression $$A$$, $$|A| = b$$ means $$A = b$$ or $$A = -b$$. 4. **Set up two equations:** $$-9 - x = 1$$ and $$-9 - x = -1$$ 5. **Solve the first equation:** $$-9 - x = 1$$ Add 9 to both sides: $$-x = 1 + 9$$ $$-x = 10$$ Multiply both sides by $$-1$$: $$x = -10$$ 6. **Solve the second equation:** $$-9 - x = -1$$ Add 9 to both sides: $$-x = -1 + 9$$ $$-x = 8$$ Multiply both sides by $$-1$$: $$x = -8$$ 7. **Final answer:** The solutions are $$x = -10$$ and $$x = -8$$.