1. **State the problem:** Solve the compound inequality $$m + 8 \leq 8 \text{ or } m + 3 \geq 12$$ and graph the solution. 2. **Solve each inequality separately:** - For $$m + 8 \leq 8$$, subtract 8 from both sides: $$m + 8 \leq 8$$ $$m + \cancel{8} - \cancel{8} \leq 8 - 8$$ $$m \leq 0$$ - For $$m + 3 \geq 12$$, subtract 3 from both sides: $$m + 3 \geq 12$$ $$m + \cancel{3} - \cancel{3} \geq 12 - 3$$ $$m \geq 9$$ 3. **Interpret the compound inequality:** The solution is all values of $$m$$ such that $$m \leq 0$$ or $$m \geq 9$$. 4. **Graph the solution:** - On a number line from 0 to 9, shade all values less than or equal to 0 (including 0). - Also shade all values greater than or equal to 9 (including 9). - The endpoints at 0 and 9 are closed dots because the inequalities include equality. **Final answer:** $$m \leq 0 \text{ or } m \geq 9$$