1. **State the problem:** We are given the inequality $$29 > 2x + 7$$ and need to answer questions about its graph and solutions. 2. **Solve the inequality:** Start by isolating $x$: $$29 > 2x + 7$$ Subtract 7 from both sides: $$29 - 7 > 2x + \cancel{7} - \cancel{7}$$ $$22 > 2x$$ Divide both sides by 2: $$\frac{22}{2} > \frac{2x}{2}$$ $$11 > x$$ This means $$x < 11$$. 3. **Graph characteristics:** - Since the inequality is strict ($<$), the graph has an **open circle** at $x=11$. - The inequality $x < 11$ means the arrow points to the **left**. 4. **Check the solutions:** - For $x=8$: Is $8 < 11$? Yes, so **true**. - For $x=11$: Is $11 < 11$? No, so **false**. - For $x=13$: Is $13 < 11$? No, so **false**. --- 5. **Second problem:** Ricky mixes white and blue paint in a ratio of 5 pints white for every 12 pints blue. Total paint combined is 56 pints. 6. **Set up the ratio:** Let $w$ = pints white, $b$ = pints blue. Given ratio: $$\frac{w}{b} = \frac{5}{12}$$ Total paint: $$w + b = 56$$ 7. **Express $w$ in terms of $b$:** $$w = \frac{5}{12}b$$ 8. **Substitute into total paint equation:** $$\frac{5}{12}b + b = 56$$ Multiply both sides by 12 to clear denominator: $$5b + 12b = 56 \times 12$$ $$17b = 672$$ 9. **Solve for $b$:** $$b = \frac{672}{17}$$ $$b = 39.53$$ (approx) 10. **Find $w$:** $$w = \frac{5}{12} \times 39.53 = 16.47$$ (approx) **Final answers:** - Graph has an **open circle** at 11. - Arrow points to the **left**. - $8$ is a **true** solution. - $11$ is **false**. - $13$ is **false**. - White paint: approximately 16.47 pints. - Blue paint: approximately 39.53 pints.