1. **Stating the problem:** Solve the inequality $$\frac{3x + 5}{2} < 10$$ for $x$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator to eliminate the fraction, being careful about the sign of the denominator. Since 2 is positive, the inequality direction remains the same. 3. **Step-by-step solution:** Multiply both sides by 2: $$\cancel{2} \times \frac{3x + 5}{\cancel{2}} < 10 \times 2$$ which simplifies to: $$3x + 5 < 20$$ 4. **Isolate $x$:** Subtract 5 from both sides: $$3x + 5 - 5 < 20 - 5$$ $$3x < 15$$ 5. **Divide both sides by 3:** $$\frac{\cancel{3}x}{\cancel{3}} < \frac{15}{3}$$ $$x < 5$$ **Final answer:** $$x < 5$$