1. **State the problem:** Solve the equation $$\frac{3}{4} + \frac{x}{3} = 5 - \frac{7}{12}$$ for $x$. 2. **Rewrite the equation:** Combine the constants on the right side: $$5 - \frac{7}{12} = \frac{60}{12} - \frac{7}{12} = \frac{53}{12}$$ So the equation becomes: $$\frac{3}{4} + \frac{x}{3} = \frac{53}{12}$$ 3. **Isolate $x$:** Subtract $\frac{3}{4}$ from both sides: $$\frac{x}{3} = \frac{53}{12} - \frac{3}{4}$$ Convert $\frac{3}{4}$ to twelfths: $$\frac{3}{4} = \frac{9}{12}$$ So: $$\frac{x}{3} = \frac{53}{12} - \frac{9}{12} = \frac{44}{12}$$ 4. **Simplify the fraction:** $$\frac{44}{12} = \frac{11}{3}$$ 5. **Solve for $x$:** Multiply both sides by 3: $$x = 3 \times \frac{11}{3}$$ Show cancellation: $$x = \cancel{3} \times \frac{11}{\cancel{3}} = 11$$ 6. **Final answer:** $$\boxed{11}$$