1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = 5$$ 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 4 to cancel the denominator: $$4 \times \frac{2x+3}{4} = 4 \times 5$$ This simplifies to: $$\cancel{4} \times \frac{2x+3}{\cancel{4}} = 20$$ So, $$2x + 3 = 20$$ 4. **Isolate $x$:** Subtract 3 from both sides: $$2x + 3 - 3 = 20 - 3$$ $$2x = 17$$ 5. **Solve for $x$:** Divide both sides by 2: $$\frac{2x}{2} = \frac{17}{2}$$ $$\cancel{2}x / \cancel{2} = \frac{17}{2}$$ $$x = \frac{17}{2}$$ 6. **Final answer:** The solution to the equation is $$x = \frac{17}{2}$$ or 8.5. This means when $x$ is 8.5, the original equation holds true.