1. **State the problem:** Solve the absolute value equation $$15 = 5|3x + 3|$$ for $x$. 2. **Isolate the absolute value expression:** Divide both sides by 5: $$\cancel{5} \times 3|3x + 3| = \cancel{5} \times 3$$ which simplifies to $$3 = |3x + 3|$$ 3. **Recall the definition of absolute value:** For $|A| = B$, where $B \geq 0$, the solutions are $A = B$ or $A = -B$. 4. **Set up two equations:** $$3x + 3 = 3$$ $$3x + 3 = -3$$ 5. **Solve each equation:** - For $3x + 3 = 3$: $$3x = 3 - 3$$ $$3x = 0$$ $$x = \frac{0}{3} = 0$$ - For $3x + 3 = -3$: $$3x = -3 - 3$$ $$3x = -6$$ $$x = \frac{-6}{3} = -2$$ 6. **Write the solutions in ascending order:** $$x = -2, 0$$ **Final answer:** $x = -2, 0$