1. **State the problem:** Solve the compound inequality $$y - 20 \geq -9 \text{ or } y - 5 \leq 2$$ and graph the solution on a number line. 2. **Solve each inequality separately:** - For $$y - 20 \geq -9$$: Add 20 to both sides: $$y - 20 + 20 \geq -9 + 20$$ $$y \geq 11$$ - For $$y - 5 \leq 2$$: Add 5 to both sides: $$y - 5 + 5 \leq 2 + 5$$ $$y \leq 7$$ 3. **Interpret the compound inequality:** The solution is all $$y$$ such that $$y \geq 11$$ or $$y \leq 7$$. This means the solution includes all values less than or equal to 7 and all values greater than or equal to 11. 4. **Graph the solution:** - Draw a number line with points at 7 and 11. - At 7, use a closed circle (because of $\leq$) and shade to the left. - At 11, use a closed circle (because of $\geq$) and shade to the right. - The region between 7 and 11 is not included. 5. **Endpoints and intervals:** - Endpoint at 7 is closed. - Endpoint at 11 is closed. - The solution is the union of two rays: $$(-\infty, 7] \cup [11, \infty)$$. **Final answer:** $$y \leq 7 \text{ or } y \geq 11$$