1. **State the problem:** Solve the inequality $3 + y > 9$. 2. **Isolate the variable:** To solve for $y$, subtract 3 from both sides: $$3 + y > 9$$ $$\cancel{3} + y > 9 - \cancel{3}$$ $$y > 6$$ 3. **Interpret the solution:** The solution is all values of $y$ greater than 6. 4. **Graph the solution:** On a number line, draw an open circle at 6 (since 6 is not included) and shade to the right to indicate all numbers greater than 6. This completes the solution for the first inequality. 2. **State the problem:** Solve the inequality $-2x \geq 8$. 2. **Isolate the variable:** Divide both sides by $-2$. Remember, dividing by a negative number reverses the inequality sign: $$-2x \geq 8$$ $$\frac{\cancel{-2}x}{\cancel{-2}} \leq \frac{8}{-2}$$ $$x \leq -4$$ 3. **Interpret the solution:** The solution is all values of $x$ less than or equal to $-4$. 4. **Graph the solution:** On a number line, draw a closed circle at $-4$ (since $-4$ is included) and shade to the left to indicate all numbers less than or equal to $-4$. This completes the solution for the second inequality.