1. **State the problem:** A warehouse starts with 460 boxes and ships out 65 boxes every week. We want to find after how many weeks the number of boxes remaining will be less than 100. 2. **Define the variable:** Let $w$ be the number of weeks. 3. **Write the inequality:** The number of boxes remaining after $w$ weeks is $460 - 65w$. We want this to be less than 100, so: $$460 - 65w < 100$$ 4. **Solve the inequality:** Subtract 460 from both sides: $$460 - 65w - 460 < 100 - 460$$ $$-65w < -360$$ 5. **Divide both sides by -65:** Remember, dividing by a negative number reverses the inequality sign. $$\cancel{-65}w > \cancel{-65} \frac{-360}{-65}$$ $$w > \frac{360}{65}$$ 6. **Simplify the fraction:** $$w > \frac{360}{65} = \frac{72}{13} \approx 5.54$$ 7. **Interpret the result:** Since $w$ must be greater than approximately 5.54, after 6 weeks the warehouse will have less than 100 boxes remaining. **Final answer:** $$\boxed{w > 5.54 \text{ weeks, so after } 6 \text{ weeks}}$$