1. **Problem 1: Solve the inequality** $3 + y > 9$ 2. **Step 1: Isolate $y$ by subtracting 3 from both sides:** $$3 + y > 9$$ $$\cancel{3} + y - \cancel{3} > 9 - 3$$ $$y > 6$$ 3. **Explanation:** We subtract 3 from both sides to keep the inequality balanced. Since we are subtracting a positive number, the inequality direction stays the same. 4. **Graphing:** On the number line, shade all values greater than 6. Use an open circle at 6 because the inequality is strict ($>$). 5. **Problem 2: Solve the inequality** $-2x \geq 8$ 6. **Step 1: Isolate $x$ by dividing both sides by $-2$:** $$-2x \geq 8$$ $$\frac{-2x}{\cancel{-2}} \leq \frac{8}{\cancel{-2}}$$ $$x \leq -4$$ 7. **Explanation:** When dividing both sides of an inequality by a negative number, the inequality sign reverses direction. 8. **Graphing:** On the number line, shade all values less than or equal to $-4$. Use a closed circle at $-4$ because the inequality includes equality ($\geq$). **Final answers:** - $y > 6$ - $x \leq -4$