https://file.aiquickdraw.com/mathbot/file/172720500776426wcbuxz.jpg

The problem in the image involves Melanie comparing the cost of purchasing DVDs from two stores. Here's a breakdown of the information:

1. **Store A** sells DVDs for $8.95 each with an additional fixed shipping fee of $9.
2. **Store B** sells DVDs for $12.35 each with no shipping fee.

Melanie wants to know how many DVDs she can order so that the total cost from Store A is no more than the total cost from Store B.

### Given Inequality
Melanie represents the situation using the inequality:
\[ 8.95d + 9 \geq 12.35d \]

### Evaluating the Inequality
- **Left Side:** $ 8.95d + 9 $ represents the cost of purchasing $ d $ DVDs from Store A, including the fixed $9 shipping fee.
- **Right Side:** $ 12.35d $ represents the cost of purchasing $ d $ DVDs from Store B, without any shipping fee.

### Analysis of the Options:
1. **Option A:** "The inequality is correct."  
   This statement is true because the given inequality accurately represents that Melanie wants the cost from Store A to be no more than (or equal to) the cost from Store B.

2. **Option B:** "The inequality symbol is incorrect."  
   This is false because the inequality symbol $ \geq $ is correct. Melanie wants the cost from Store A to be no more than the cost from Store B.

3. **Option C:** "The left side should be $ 8.95(d + 9) $."  
   This is incorrect. It mistakenly adds the shipping fee of 9 into the cost per DVD, which is not how the cost is calculated.

4. **Option D:** "The right side should be $ 12.35 + d $."  
   This is incorrect because it represents an incorrect formula for the cost from Store B.

### Conclusion
The correct answer is **Option A: The inequality is correct.**

Would you like more details or have any questions about this solution? 

### Related Questions
1. What is the maximum number of DVDs Melanie can order so that the cost from Store A is still cheaper than Store B?
2. How would the inequality change if Store A reduced their shipping fee to $5?
3. What would the total cost be for 5 DVDs from each store?
4. If Store B offers a discount of $2 per DVD, how does the inequality change?
5. Can you graph the inequality to visually show the comparison between the two stores' costs?

**Tip:** When comparing costs, always ensure you separate variable costs (like cost per DVD) from fixed costs (like shipping fees).

Melanie is ordering used DVDs online. Store A sells used DVDs for $8.95 each, plus $9 for shipping, no matter how many DVDs you order. Store B sells used DVDs for $12.35 each, with no shipping cost. Melanie wants to know how many DVDs she can order so that the cost from Store A is no more than Store B. Melanie represents the problem with the inequality 8.95d + 9 ≥ 12.35d. Which of the following best describes the inequality?

Learn how to solve an inequality comparing the costs of DVDs from two different stores, with shipping fees and different price points per DVD. Suitable for students in Grades 8-9. Explore how algebraic inequalities represent real-world scenarios.

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