1. **State the problem:** Solve the inequality $-17 - 4x > -37$ for $x$. 2. **Isolate the variable term:** Add 17 to both sides to move the constant term on the left side. $$-17 - 4x + 17 > -37 + 17$$ This simplifies to: $$-4x > -20$$ 3. **Divide both sides by -4:** When dividing or multiplying an inequality by a negative number, the inequality sign reverses. $$\cancel{-4}x \div \cancel{-4} < \frac{-20}{-4}$$ This gives: $$x < 5$$ 4. **Final answer:** The solution to the inequality is $$x < 5$$ This means all values of $x$ less than 5 satisfy the inequality.