1. **State the problem:** We have three vegetable patches with areas: - Jake's patch: $h$ - Aliya's patch: $3h + 7$ - Lucy's patch: $5h$ The total area is greater than 79 m$^2$. We need to write and solve an inequality for $h$. 2. **Write the inequality:** The total area is the sum of all three patches: $$h + (3h + 7) + 5h > 79$$ 3. **Simplify the inequality:** Combine like terms: $$h + 3h + 7 + 5h > 79$$ $$9h + 7 > 79$$ 4. **Solve for $h$:** Subtract 7 from both sides: $$9h > 79 - 7$$ $$9h > 72$$ Divide both sides by 9: $$h > \frac{72}{9}$$ $$h > 8$$ 5. **Interpretation:** The value of $h$ must be greater than 8 for the total area to be greater than 79 m$^2$. **Final answer:** $$h > 8$$