Inequality Graph A31Cb7

1. **State the problem:** We need to find the solution set for the inequality $$-3q + 11 \geq 38$$ or $$-2q + 39 < 45$$ and determine which graph represents this solution. 2. **Solve the first inequality:** $$-3q + 11 \geq 38$$ Subtract 11 from both sides: $$-3q + 11 - 11 \geq 38 - 11$$ $$-3q \geq 27$$ Divide both sides by $$-3$$, remembering to reverse the inequality sign because we divide by a negative number: $$q \leq \frac{27}{-3}$$ $$q \leq -9$$ 3. **Solve the second inequality:** $$-2q + 39 < 45$$ Subtract 39 from both sides: $$-2q + 39 - 39 < 45 - 39$$ $$-2q < 6$$ Divide both sides by $$-2$$, reversing the inequality sign: $$q > \frac{6}{-2}$$ $$q > -3$$ 4. **Combine the solution sets:** The solution is $$q \leq -9$$ or $$q > -3$$. 5. **Interpret the solution on a number line:** - For $$q \leq -9$$, the point at $$-9$$ is included (closed circle) and shading is to the left. - For $$q > -3$$, the point at $$-3$$ is not included (open circle) and shading is to the right. 6. **Match with the graphs:** - Left graph: open circle at $$-9$$ and closed circle at $$-3$$, shading left of $$-9$$ and right of $$-3$$. - Middle graph: closed circles at both $$-9$$ and $$-3$$, shading left of $$-9$$ and right of $$-3$$. - Right graph: closed circle at $$-9$$ and open circle at $$-3$$, shading left of $$-9$$ and right of $$-3$$. 7. **Conclusion:** The correct graph is the **right graph** because it correctly shows $$q \leq -9$$ (closed circle at $$-9$$) and $$q > -3$$ (open circle at $$-3$$) with shading in the correct directions. **Final answer:** Right graph represents the solution.