1. **State the problem:** Solve the equation $$\frac{w+7}{4} = \frac{w-5}{3}$$ for $w$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the least common denominator (LCD) to eliminate fractions. 3. **Find the LCD:** The denominators are 4 and 3, so the LCD is 12. 4. **Multiply both sides by 12:** $$12 \times \frac{w+7}{4} = 12 \times \frac{w-5}{3}$$ 5. **Simplify each side:** $$\cancel{12}^{3} \times \frac{w+7}{\cancel{4}^{1}} = \cancel{12}^{4} \times \frac{w-5}{\cancel{3}^{1}}$$ which simplifies to $$3(w+7) = 4(w-5)$$ 6. **Distribute:** $$3w + 21 = 4w - 20$$ 7. **Bring variables to one side and constants to the other:** $$3w - 4w = -20 - 21$$ 8. **Simplify:** $$-w = -41$$ 9. **Divide both sides by -1:** $$\frac{-w}{-1} = \frac{-41}{-1}$$ which simplifies to $$w = 41$$ **Final answer:** $$w = 41$$