1. **State the problem:** Solve the compound inequality $$j - 16 > -10 \text{ or } 2j + 5 \leq -7$$ and graph the solution. 2. **Solve the first inequality:** $$j - 16 > -10$$ Add 16 to both sides: $$\cancel{j} - 16 + 16 > -10 + 16$$ $$j > 6$$ 3. **Solve the second inequality:** $$2j + 5 \leq -7$$ Subtract 5 from both sides: $$2j + \cancel{5} - 5 \leq -7 - 5$$ $$2j \leq -12$$ Divide both sides by 2: $$\frac{2j}{\cancel{2}} \leq \frac{-12}{2}$$ $$j \leq -6$$ 4. **Combine the solutions:** The solution is $$j > 6 \text{ or } j \leq -6$$. 5. **Graph the solution:** - For $$j > 6$$, draw an open circle at 6 and shade to the right. - For $$j \leq -6$$, draw a closed circle at -6 and shade to the left. This represents all values of $$j$$ that satisfy either inequality. **Final answer:** $$j > 6 \text{ or } j \leq -6$$