1. **State the problem:** Solve the inequality $$-3x + 12 > 27$$. 2. **Isolate the variable term:** Subtract 12 from both sides to get $$-3x > 27 - 12$$. 3. Simplify the right side: $$-3x > 15$$. 4. **Divide both sides by -3:** When dividing by a negative number, remember to reverse the inequality sign. $$x < \frac{15}{-3}$$ 5. Simplify the fraction: $$x < -5$$. **Final answer:** $$x < -5$$. This corresponds to option b. The key rule is that dividing or multiplying an inequality by a negative number reverses the inequality sign.