1. **State the problem:** Solve the inequality $-2x - 76 > -66$. 2. **Isolate the variable term:** Add 76 to both sides to get rid of the constant on the left. $$-2x - 76 + 76 > -66 + 76$$ $$-2x > 10$$ 3. **Divide both sides by -2:** When dividing or multiplying an inequality by a negative number, remember to reverse the inequality sign. $$x < \frac{10}{-2}$$ $$x < -5$$ 4. **Interpretation:** The solution is all $x$ values less than $-5$. 5. **Number line:** On the number line, this means shading all points to the left of $-5$ (not including $-5$ itself). **Final answer:** $$x < -5$$