1. **State the problem:** A warehouse starts with 7,250 books and ships out 150 books per day. We want to find when the number of books will be less than 2,000, so the warehouse will start printing more books.
2. **Define variables and write the inequality:** Let $d$ be the number of days. The number of books left after $d$ days is given by:
$$7250 - 150d$$
We want to find when this is less than 2,000:
$$7250 - 150d < 2000$$
3. **Solve the inequality:**
Subtract 7250 from both sides:
$$\cancel{7250} - 150d - \cancel{7250} < 2000 - 7250$$
$$-150d < -5250$$
4. **Divide both sides by -150:**
Remember, dividing by a negative number reverses the inequality sign:
$$\frac{-150d}{-150} > \frac{-5250}{-150}$$
$$d > 35$$
5. **Interpret the solution:** The warehouse will start printing more books after more than 35 days.
6. **Check if printing occurs on the 30th day:** Since $30 \not> 35$, the warehouse will not be printing more books on the 30th day.
**Final answer:**
The warehouse will print more books when $d > 35$. On day 30, it will not be printing more books yet.
Warehouse Books 53E817
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