1. **State the problem:** Solve the equation $$\frac{23}{2} = \frac{4x - 3}{2}$$ for $x$. 2. **Understand the equation:** We have two fractions equal to each other: $$\frac{23}{2} = \frac{4x - 3}{2}$$. 3. **Use the property of equality of fractions:** If $$\frac{a}{b} = \frac{c}{b}$$ and $b \neq 0$, then $a = c$. 4. **Apply this property:** Since denominators are equal and non-zero, set numerators equal: $$23 = 4x - 3$$ 5. **Solve for $x$:** Add 3 to both sides: $$23 + 3 = 4x - 3 + 3$$ $$26 = 4x$$ 6. **Divide both sides by 4:** $$\frac{26}{\cancel{4}} = x \cdot \frac{\cancel{4}}{4}$$ $$x = \frac{26}{4}$$ 7. **Simplify the fraction:** $$x = \frac{13}{2}$$ **Final answer:** $$x = \frac{13}{2}$$