1. **State the problem:** We are given the inequality $$100 + 25x < 150 + 20x$$ where $x$ represents the number of hours a moving job takes. We want to find for which values of $x$ company A (costing $100 + 25x$) is less expensive than company B (costing $150 + 20x$). 2. **Write the inequality and isolate $x$:** $$100 + 25x < 150 + 20x$$ 3. **Subtract $20x$ from both sides:** $$100 + 25x - 20x < 150 + 20x - 20x$$ $$100 + 5x < 150$$ 4. **Subtract 100 from both sides:** $$100 + 5x - 100 < 150 - 100$$ $$5x < 50$$ 5. **Divide both sides by 5:** $$x < 10$$ 6. **Interpretation:** This means company A is less expensive than company B when the job takes less than 10 hours. 7. **Check the boundary:** At $x=10$, costs are equal: $$100 + 25(10) = 100 + 250 = 350$$ $$150 + 20(10) = 150 + 200 = 350$$ 8. **Summary:** - For $x < 10$, company A is cheaper. - For $x = 10$, costs are equal. - For $x > 10$, company B is cheaper. This helps decide which company to choose based on the job duration.