1. **State the problem:** Solve the inequality $$-5 < 1 + \frac{3}{2}(-4x + 6)$$ for $x$. 2. **Recall the distributive property:** Multiply $\frac{3}{2}$ by each term inside the parentheses. 3. **Apply the distributive property:** $$-5 < 1 + \frac{3}{2} \times (-4x) + \frac{3}{2} \times 6$$ $$-5 < 1 - 6x + 9$$ 4. **Combine like terms on the right side:** $$-5 < 10 - 6x$$ 5. **Isolate the variable term:** Subtract 10 from both sides. $$-5 - 10 < 10 - 6x - 10$$ $$-15 < -6x$$ 6. **Divide both sides by $-6$ to solve for $x$:** Remember, dividing by a negative number reverses the inequality sign. $$\frac{-15}{\cancel{-6}} \; \cancel{<} \; \frac{-6x}{\cancel{-6}}$$ $$\frac{15}{6} > x$$ 7. **Simplify the fraction:** $$\frac{15}{6} = \frac{5}{2}$$ 8. **Final solution:** $$x < \frac{5}{2}$$ **Answer:** The solution set is $$x < \frac{5}{2}$$.