1. **State the problem:** Solve the inequality $$9 + 3(-3t + 10) \leq 6t + 8 - 4$$ for $t$ and write the answer in simplest form. 2. **Apply the distributive property:** Multiply $3$ by each term inside the parentheses: $$9 + 3 \times (-3t) + 3 \times 10 \leq 6t + 8 - 4$$ which simplifies to $$9 - 9t + 30 \leq 6t + 8 - 4$$ 3. **Combine like terms on the left and right sides:** $$9 + 30 = 39$$ $$8 - 4 = 4$$ So the inequality becomes $$39 - 9t \leq 6t + 4$$ 4. **Bring all terms involving $t$ to one side and constants to the other:** Add $9t$ to both sides: $$39 - \cancel{9t} + 9t \leq 6t + 9t + 4$$ which simplifies to $$39 \leq 15t + 4$$ Subtract $4$ from both sides: $$39 - 4 \leq 15t + \cancel{4} - 4$$ which simplifies to $$35 \leq 15t$$ 5. **Isolate $t$ by dividing both sides by 15:** $$\frac{35}{\cancel{15}} \leq \frac{15t}{\cancel{15}}$$ which simplifies to $$\frac{35}{15} \leq t$$ 6. **Simplify the fraction:** $$\frac{35}{15} = \frac{7}{3}$$ 7. **Write the solution:** $$t \geq \frac{7}{3}$$ **Note:** The original problem states the answer as $t < $ something, but solving the inequality gives $t \geq \frac{7}{3}$. This is the correct solution based on the inequality given. **Final answer:** $$t \geq \frac{7}{3}$$