1. **Problem Statement:** 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. **Step 1: Eliminate the denominator by multiplying both sides by 4:** $$4 \times \frac{2x+3}{4} = 4 \times 5$$ This simplifies to: $$\cancel{4} \times \frac{2x+3}{\cancel{4}} = 20$$ $$2x + 3 = 20$$ 4. **Step 2: Subtract 3 from both sides to isolate the term with $x$:** $$2x + 3 - 3 = 20 - 3$$ $$2x = 17$$ 5. **Step 3: Divide both sides by 2 to solve for $x$:** $$\frac{2x}{2} = \frac{17}{2}$$ $$\cancel{2}x / \cancel{2} = \frac{17}{2}$$ $$x = \frac{17}{2}$$ 6. **Final answer:** $$x = \frac{17}{2}$$ or 8.5. This means the value of $x$ that satisfies the equation is $8.5$.