1. **State the problem:** Solve the equation $$3|x - 5| = 12$$ for $$x$$. 2. **Isolate the absolute value:** Divide both sides by 3 to get $$|x - 5| = \frac{12}{3}$$. 3. **Simplify the division:** $$|x - 5| = \cancel{\frac{12}{3}}{4}$$ 4. **Understand absolute value:** The equation $$|A| = B$$ means $$A = B$$ or $$A = -B$$. 5. **Set up two linear equations:** $$x - 5 = 4$$ $$x - 5 = -4$$ 6. **Solve the first equation:** Add 5 to both sides: $$x - 5 + 5 = 4 + 5$$ $$x = 9$$ 7. **Solve the second equation:** Add 5 to both sides: $$x - 5 + 5 = -4 + 5$$ $$x = 1$$ **Final answer:** $$x = 9$$ or $$x = 1$$