1. The problem is to solve the equation $$3|2x - 7| = 15$$ for $x$. 2. First, isolate the absolute value expression by dividing both sides by 3: $$|2x - 7| = \frac{15}{3} = 5$$ 3. Recall that if $|A| = B$ where $B > 0$, then $A = B$ or $A = -B$. 4. Apply this rule to our equation: $$2x - 7 = 5 \quad \text{or} \quad 2x - 7 = -5$$ 5. Solve each linear equation separately: - For $2x - 7 = 5$: $$2x = 5 + 7 = 12$$ $$x = \frac{12}{2} = 6$$ - For $2x - 7 = -5$: $$2x = -5 + 7 = 2$$ $$x = \frac{2}{2} = 1$$ 6. Therefore, the solution set is $$\{1, 6\}$$. 7. This means the values of $x$ that satisfy the original equation are 1 and 6.