1. **State the problem:** Solve the inequality $$-45 \leq m + 27 - 9m \leq -29$$. 2. **Simplify the inequality:** Combine like terms inside the inequality. $$m + 27 - 9m = -8m + 27$$ So the inequality becomes: $$-45 \leq -8m + 27 \leq -29$$ 3. **Isolate the variable term:** Subtract 27 from all parts of the inequality. $$-45 - 27 \leq -8m + 27 - 27 \leq -29 - 27$$ $$-72 \leq -8m \leq -56$$ 4. **Divide by -8:** Since we are dividing by a negative number, reverse the inequality signs. $$\frac{-72}{-8} \geq m \geq \frac{-56}{-8}$$ $$9 \geq m \geq 7$$ 5. **Rewrite the solution:** The solution is $$7 \leq m \leq 9$$ This means $m$ is between 7 and 9 inclusive. **Final answer:** $$7 \leq m \leq 9$$