1. **State the problem:** Solve the inequality $$3q - 9 \leq 8q + 10$$ for $q$ and write the answer in simplest form. 2. **Write the inequality:** $$3q - 9 \leq 8q + 10$$ 3. **Isolate variable terms on one side:** Subtract $3q$ from both sides: $$3q - 9 - 3q \leq 8q + 10 - 3q$$ $$\cancel{3q} - 9 \leq 5q + 10$$ 4. **Isolate constants on the other side:** Subtract $10$ from both sides: $$-9 - 10 \leq 5q + 10 - 10$$ $$-19 \leq 5q + \cancel{10}$$ 5. **Rewrite inequality:** $$-19 \leq 5q$$ 6. **Divide both sides by 5 to solve for $q$:** Since 5 is positive, inequality direction stays the same. $$\frac{-19}{\cancel{5}} \leq \frac{5q}{\cancel{5}}$$ $$-\frac{19}{5} \leq q$$ 7. **Rewrite in standard form:** $$q \geq -\frac{19}{5}$$ **Final answer:** $$q \geq -\frac{19}{5}$$