1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the least common denominator (LCD) to eliminate fractions. 3. **Find the LCD:** The denominators are 4 and 2, so the LCD is 4. 4. **Multiply both sides by 4:** $$4 \times \frac{2x+3}{4} = 4 \times \frac{x-1}{2}$$ 5. **Simplify:** $$\cancel{4} \times \frac{2x+3}{\cancel{4}} = 2 \times (x-1)$$ $$2x + 3 = 2x - 2$$ 6. **Subtract $2x$ from both sides:** $$2x + 3 - 2x = 2x - 2 - 2x$$ $$3 = -2$$ 7. **Analyze the result:** The statement $3 = -2$ is false, which means there is no solution. **Final answer:** There is no solution to the equation.