1. **State the problem:** Simplify and solve the equation $8 (x - 2) - 5 (3 - x) + 16 = 15 - 4 (3 - x)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$8x - 16 - 15 + 5x + 16 = 15 - 12 + 4x$$ 3. **Combine like terms on each side:** On the left side, combine $-16$, $-15$, and $16$. On the right side, combine $15$ and $-12$. $$8x + 5x - 15 = 3 + 4x$$ 4. **Simplify further:** $$13x - 15 = 3 + 4x$$ 5. **Isolate variable terms on one side:** Subtract $4x$ from both sides. $$13x - \cancel{4x} - 15 = 3 + \cancel{4x}$$ $$9x - 15 = 3$$ 6. **Isolate the constant term:** Add $15$ to both sides. $$9x - \cancel{15} + 15 = 3 + 15$$ $$9x = 18$$ 7. **Solve for $x$ by dividing both sides by 9:** $$\frac{9x}{\cancel{9}} = \frac{18}{\cancel{9}}$$ $$x = 2$$ **Final answer:** $x = 2$