1. **State the problem:** Solve the inequality $$5h + 5(9h + 1) \leq 5h + 1 - 2$$ for $h$. 2. **Apply the distributive property:** Multiply $5$ by each term inside the parentheses: $$5h + 5 \times 9h + 5 \times 1 \leq 5h + 1 - 2$$ which simplifies to $$5h + 45h + 5 \leq 5h + 1 - 2$$ 3. **Combine like terms on the left side:** $$50h + 5 \leq 5h + (1 - 2)$$ $$50h + 5 \leq 5h - 1$$ 4. **Subtract $5h$ from both sides to isolate $h$ terms on one side:** $$50h - 5h + 5 \leq -1$$ $$45h + 5 \leq -1$$ 5. **Subtract 5 from both sides:** $$45h \leq -1 - 5$$ $$45h \leq -6$$ 6. **Divide both sides by 45:** Since 45 is positive, the inequality direction stays the same: $$h \leq \frac{-6}{45}$$ 7. **Simplify the fraction:** $$h \leq \frac{-2}{15}$$ **Final answer:** $$\boxed{h \leq -\frac{2}{15}}$$