1. **Problem:** Solve the inequality $$\frac{2x + 3}{2} > \frac{x - 4}{3}$$. 2. **Formula and rules:** To solve inequalities involving fractions, first find a common denominator or cross-multiply, keeping in mind that if you multiply or divide by a negative number, the inequality sign reverses. 3. **Step-by-step solution:** 1. Start with the inequality: $$\frac{2x + 3}{2} > \frac{x - 4}{3}$$ 2. Cross-multiply (both denominators are positive, so inequality direction stays the same): $$3(2x + 3) > 2(x - 4)$$ 3. Expand both sides: $$6x + 9 > 2x - 8$$ 4. Subtract $$2x$$ from both sides: $$6x - 2x + 9 > -8$$ $$4x + 9 > -8$$ 5. Subtract 9 from both sides: $$4x > -17$$ 6. Divide both sides by 4 (positive number, inequality stays the same): $$x > -\frac{17}{4}$$ 4. **Final answer:** $$x > -4.25$$ This means any $$x$$ greater than $$-4.25$$ satisfies the inequality.