1. **State the problem:** Solve the compound inequality $$m + 8 \leq 8 \text{ or } m + 3 \geq 12$$ and graph the solution on a number line. 2. **Solve each inequality separately:** - For $$m + 8 \leq 8$$: $$m + 8 \leq 8$$ Subtract 8 from both sides: $$m + \cancel{8} - \cancel{8} \leq 8 - 8$$ $$m \leq 0$$ - For $$m + 3 \geq 12$$: $$m + 3 \geq 12$$ Subtract 3 from both sides: $$m + \cancel{3} - \cancel{3} \geq 12 - 3$$ $$m \geq 9$$ 3. **Combine the solutions:** The solution is all values of $$m$$ such that $$m \leq 0$$ or $$m \geq 9$$. 4. **Graph the solution:** - Draw a number line from 0 to 9. - For $$m \leq 0$$, shade all values to the left of 0 including 0 (closed circle at 0). - For $$m \geq 9$$, shade all values to the right of 9 including 9 (closed circle at 9). - The middle section between 0 and 9 is not included. 5. **Endpoints:** - The endpoints 0 and 9 are included (closed circles). - You can change an endpoint to open by selecting the circle and toggling it. - You can delete segments by selecting the middle of the segment or ray. **Final answer:** $$m \leq 0 \text{ or } m \geq 9$$