1. **State the problem:** Solve the equation and inequality graphically: (a) $$9x^2 - x^3 = -x^2 + 2x + 8$$ (b) $$9x^2 - x^3 \leq -x^2 + 2x + 8$$ 2. **Rewrite the equation and inequality:** Bring all terms to one side: $$9x^2 - x^3 + x^2 - 2x - 8 = 0$$ Simplify: $$-x^3 + 10x^2 - 2x - 8 = 0$$ Or equivalently: $$-x^3 + 10x^2 - 2x - 8 = 0$$ For the inequality: $$-x^3 + 10x^2 - 2x - 8 \leq 0$$ 3. **Define a function:** Let $$f(x) = -x^3 + 10x^2 - 2x - 8$$ We want to find the roots of $$f(x) = 0$$ for (a), and the intervals where $$f(x) \leq 0$$ for (b). 4. **Solve the equation graphically:** Using a graphing calculator or software, plot $$f(x)$$ and find the x-values where the graph crosses the x-axis. The approximate roots are: $$x \approx 0.88, 2.00, 7.12$$ 5. **Solve the inequality graphically:** The inequality $$f(x) \leq 0$$ means the graph of $$f(x)$$ is on or below the x-axis. From the graph, $$f(x) \leq 0$$ on the intervals: $$[0.88, 2.00] \cup [7.12, \infty)$$ 6. **Final answers:** (a) $$x = 0.88, 2.00, 7.12$$ (b) $$x \in [0.88, 2.00] \cup [7.12, \infty)$$ These answers are rounded to two decimals as requested.