1. **State the problem:** Solve the equation $$|3x| = 3$$. 2. **Recall the definition of absolute value:** For any real number $a$, $$|a| = b$$ means $$a = b$$ or $$a = -b$$, where $b \geq 0$. 3. **Apply this to the equation:** Since $$|3x| = 3$$, we have two cases: - Case 1: $$3x = 3$$ - Case 2: $$3x = -3$$ 4. **Solve Case 1:** $$3x = 3$$ Divide both sides by 3: $$\cancel{3}x = \cancel{3}$$ $$x = 1$$ 5. **Solve Case 2:** $$3x = -3$$ Divide both sides by 3: $$\cancel{3}x = \cancel{-3}$$ $$x = -1$$ 6. **Final answer:** The solutions to the equation $$|3x| = 3$$ are $$x = 1$$ and $$x = -1$$.