1. **State the problem:** Jessica is building a model skyscraper with each floor 4 inches tall and an 8-inch spire on top. The total height must be at least 50 inches. We need to find the minimum number of floors, $x$, she needs. 2. **Set up the inequality:** The total height is the height of the floors plus the spire height. So, $$4x + 8 \geq 50$$ where $x$ is the number of floors. 3. **Solve the inequality:** Subtract 8 from both sides: $$4x + \cancel{8} - \cancel{8} \geq 50 - 8$$ $$4x \geq 42$$ Divide both sides by 4: $$\frac{4x}{\cancel{4}} \geq \frac{42}{\cancel{4}}$$ $$x \geq 10.5$$ 4. **Interpret the result:** Since $x$ represents the number of floors and must be a whole number, Jessica needs at least 11 floors to meet the height requirement. **Final answer:** Jessica needs to make at least **11 floors**.