1. **State the problem:** Solve the compound inequality $$t + 17 \leq 18 \text{ or } \frac{t + 16}{3} > 6$$ and graph the solution on a number line from 0 to 9. 2. **Solve the first inequality:** $$t + 17 \leq 18$$ Subtract 17 from both sides: $$\cancel{t + 17} - 17 \leq 18 - 17$$ $$t \leq 1$$ 3. **Solve the second inequality:** $$\frac{t + 16}{3} > 6$$ Multiply both sides by 3: $$\cancel{\frac{t + 16}{3}} \times 3 > 6 \times 3$$ $$t + 16 > 18$$ Subtract 16 from both sides: $$\cancel{t + 16} - 16 > 18 - 16$$ $$t > 2$$ 4. **Combine the solutions:** The compound inequality uses "or," so the solution is all values where either inequality is true: $$t \leq 1 \quad \text{or} \quad t > 2$$ 5. **Interpret the solution:** - For $$t \leq 1$$, the solution includes all numbers less than or equal to 1. - For $$t > 2$$, the solution includes all numbers greater than 2. 6. **Graph the solution:** - On the number line from 0 to 9, shade all points less than or equal to 1 (including 1, so a closed circle at 1). - Also shade all points greater than 2 (open circle at 2, shading to the right). **Final answer:** $$\boxed{t \leq 1 \text{ or } t > 2}$$