1. **State the problem:** We want to solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by the denominator to eliminate the fraction. 3. **Multiply both sides by 3:** $$3 \times \frac{2x+4}{3} = 3 \times 5$$ 4. **Cancel the denominator:** $$\cancel{3} \times \frac{2x+4}{\cancel{3}} = 15$$ 5. **Simplify:** $$2x + 4 = 15$$ 6. **Subtract 4 from both sides:** $$2x + 4 - 4 = 15 - 4$$ $$2x = 11$$ 7. **Divide both sides by 2:** $$\frac{2x}{2} = \frac{11}{2}$$ $$\cancel{2}x / \cancel{2} = \frac{11}{2}$$ 8. **Simplify:** $$x = \frac{11}{2}$$ **Final answer:** $$x = \frac{11}{2}$$