1. **State the problem:** Solve the first inequality $-3 - 7x > -17$ for $x$. 2. **Write the inequality:** $$-3 - 7x > -17$$ 3. **Add 3 to both sides to isolate the term with $x$:** $$-3 - 7x + 3 > -17 + 3$$ $$\cancel{-3} - 7x + \cancel{3} > -17 + 3$$ $$-7x > -14$$ 4. **Divide both sides by $-7$ to solve for $x$.** Remember, dividing by a negative number reverses the inequality sign: $$\frac{-7x}{-7} < \frac{-14}{-7}$$ $$\cancel{-7}x / \cancel{-7} < -14 / -7$$ $$x < 2$$ 5. **Final answer:** $$x < 2$$ This means $x$ must be less than 2 to satisfy the inequality. **Note:** Although there are three inequalities given, per instructions, only the first inequality is solved here.