1. **State the problem:** Solve the equation $$|3x| = 24$$ for $x$. 2. **Recall the absolute value property:** For any real number $a$, $$|a| = b$$ implies $$a = b$$ or $$a = -b$$. 3. **Apply the property to the equation:** $$|3x| = 24 \implies 3x = 24 \text{ or } 3x = -24$$ 4. **Solve each equation for $x$:** - For $$3x = 24$$, divide both sides by 3: $$x = \frac{24}{3}$$ - For $$3x = -24$$, divide both sides by 3: $$x = \frac{-24}{3}$$ 5. **Show the cancellation explicitly:** $$x = \frac{\cancel{3}8}{\cancel{3}} = 8$$ $$x = \frac{\cancel{3}(-8)}{\cancel{3}} = -8$$ 6. **Final answer:** $$x = 8 \text{ or } x = -8$$