1. **State the problem:** Solve the equation $$|2x - 13| = 15$$ for $x$. 2. **Recall the definition of absolute value:** For any expression $A$, $$|A| = B$$ means $$A = B \text{ or } A = -B$$. 3. **Apply this to our problem:** $$2x - 13 = 15 \quad \text{or} \quad 2x - 13 = -15$$ 4. **Solve each equation separately:** - For $$2x - 13 = 15$$: $$2x = 15 + 13$$ $$2x = 28$$ $$x = \frac{28}{2}$$ $$x = 14$$ - For $$2x - 13 = -15$$: $$2x = -15 + 13$$ $$2x = -2$$ $$x = \frac{-2}{2}$$ $$x = -1$$ 5. **Final answer:** $$x = 14 \quad \text{or} \quad x = -1$$ These are the two solutions to the equation.