1. **State the problem:** Solve the compound inequality $$5k + 9 \geq 14$$ or $$-7k - 5 \geq 2$$ and graph the solution on a number line. 2. **Solve the first inequality:** $$5k + 9 \geq 14$$ Subtract 9 from both sides: $$5k + \cancel{9} - 9 \geq 14 - 9$$ $$5k \geq 5$$ Divide both sides by 5: $$\frac{5k}{\cancel{5}} \geq \frac{5}{\cancel{5}}$$ $$k \geq 1$$ 3. **Solve the second inequality:** $$-7k - 5 \geq 2$$ Add 5 to both sides: $$-7k - \cancel{5} + 5 \geq 2 + 5$$ $$-7k \geq 7$$ Divide both sides by -7 (remember to reverse the inequality sign when dividing by a negative): $$\frac{-7k}{\cancel{-7}} \leq \frac{7}{\cancel{-7}}$$ $$k \leq -1$$ 4. **Combine the solutions:** The solution is $$k \geq 1$$ or $$k \leq -1$$. 5. **Graph the solution:** - For $$k \geq 1$$, draw a closed circle at 1 and shade to the right (since it includes 1). - For $$k \leq -1$$, draw a closed circle at -1 and shade to the left. **Final answer:** $$k \leq -1$$ or $$k \geq 1$$