1. **State the problem:** Solve the compound inequality $$5 \geq \frac{3n - 2}{2} \geq -10$$ and graph the solution. 2. **Understand the inequality:** This means $$\frac{3n - 2}{2}$$ is between $$-10$$ and $$5$$ inclusive. 3. **Break into two inequalities:** $$5 \geq \frac{3n - 2}{2}$$ and $$\frac{3n - 2}{2} \geq -10$$ 4. **Solve the first inequality:** Multiply both sides by 2 (positive, so inequality signs stay the same): $$5 \times 2 \geq \cancel{2} \times \frac{3n - 2}{\cancel{2}}$$ $$10 \geq 3n - 2$$ Add 2 to both sides: $$10 + 2 \geq 3n$$ $$12 \geq 3n$$ Divide both sides by 3: $$\frac{12}{\cancel{3}} \geq \frac{3n}{\cancel{3}}$$ $$4 \geq n$$ 5. **Solve the second inequality:** Multiply both sides by 2: $$\cancel{2} \times \frac{3n - 2}{\cancel{2}} \geq -10 \times 2$$ $$3n - 2 \geq -20$$ Add 2 to both sides: $$3n \geq -20 + 2$$ $$3n \geq -18$$ Divide both sides by 3: $$\frac{3n}{\cancel{3}} \geq \frac{-18}{\cancel{3}}$$ $$n \geq -6$$ 6. **Combine the results:** $$-6 \leq n \leq 4$$ 7. **Interpretation:** The solution is all values of $$n$$ between $$-6$$ and $$4$$ inclusive. 8. **Graphing:** On a number line from $$-10$$ to $$4$$, mark the points $$-6$$ and $$4$$ with closed dots (since the inequalities are inclusive). Shade the region between $$-6$$ and $$4$$. **Final answer:** $$\boxed{-6 \leq n \leq 4}$$