1. **State the problem:** Solve the inequality $-4x < 12$ for $x$. 2. **Recall the rule:** When dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be reversed. 3. **Divide both sides by $-4$:** $$-4x < 12$$ Divide both sides by $\cancel{-4}$ (remember to reverse the inequality): $$x > \frac{12}{\cancel{-4}}$$ 4. **Simplify the fraction:** $$x > -3$$ 5. **Final answer:** The solution to the inequality is $x > -3$. This means $x$ can be any number greater than $-3$.