1. **State the problem:** Solve the equation $$\frac{3x - 16}{3} = \frac{5x + 7}{4}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the least common denominator (LCD) to eliminate the denominators. 3. **Find the LCD:** The denominators are 3 and 4, so the LCD is 12. 4. **Multiply both sides by 12:** $$12 \times \frac{3x - 16}{3} = 12 \times \frac{5x + 7}{4}$$ 5. **Simplify each side:** $$\cancel{12} \times \frac{3x - 16}{\cancel{3}} = \cancel{12} \times \frac{5x + 7}{\cancel{4}}$$ $$4(3x - 16) = 3(5x + 7)$$ 6. **Distribute:** $$12x - 64 = 15x + 21$$ 7. **Bring variables to one side and constants to the other:** $$12x - 15x = 21 + 64$$ $$-3x = 85$$ 8. **Divide both sides by -3:** $$\frac{-3x}{\cancel{-3}} = \frac{85}{\cancel{-3}}$$ $$x = -\frac{85}{3}$$ **Final answer:** $$x = -\frac{85}{3}$$