1. **State the problem:** Solve the inequality $w \leq 1$ and $w > 3 \frac{1}{2}$. 2. **Analyze the inequalities:** - $w \leq 1$ means $w$ is less than or equal to 1. - $w > 3 \frac{1}{2}$ means $w$ is greater than 3.5. 3. **Check for overlap:** The two inequalities require $w$ to be simultaneously less than or equal to 1 and greater than 3.5. 4. **Conclusion:** No number can satisfy both conditions at the same time. 5. **Final answer:** $$\boxed{\text{No solution}}$$ 1. **State the problem:** Solve the compound inequality $45.5 \leq 7c \leq -21$. 2. **Analyze the inequality:** This means $7c$ is greater than or equal to 45.5 and at the same time less than or equal to -21. 3. **Check for overlap:** $7c$ cannot be both greater than or equal to 45.5 and less than or equal to -21 simultaneously. 4. **Conclusion:** No value of $c$ satisfies this compound inequality. 5. **Final answer:** $$\boxed{\text{No solution}}$$