1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We can do this by eliminating the denominator and then solving the resulting linear equation. 3. **Eliminate the denominator:** Multiply both sides of the equation by 3 to cancel the denominator: $$3 \times \frac{2x+4}{3} = 3 \times 5$$ This simplifies to: $$\cancel{3} \times \frac{2x+4}{\cancel{3}} = 15$$ which is: $$2x + 4 = 15$$ 4. **Isolate $x$:** Subtract 4 from both sides: $$2x + 4 - 4 = 15 - 4$$ $$2x = 11$$ 5. **Solve for $x$:** Divide both sides by 2: $$\frac{2x}{2} = \frac{11}{2}$$ $$\cancel{2}x/\cancel{2} = \frac{11}{2}$$ $$x = \frac{11}{2}$$ **Final answer:** $$x = \frac{11}{2}$$