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In this problem, Isabella needs to determine how many sets of glasses to purchase to ensure the restaurant has at least 510 glasses. Currently, there are 231 glasses available. Each set she can buy contains 18 glasses. To find the minimum number of sets \(x\) she should buy, we set up an inequality that accounts for the glasses currently available plus the glasses from the new sets being at least 510.

The inequality to represent this situation is:
\[ 231 + 18x \geq 510 \]

This inequality means that the current glasses plus 18 times the number of sets she buys should be at least 510. The correct option to represent this inequality is:
\[ 510 \geq 231 + 18x \]

This option might look a bit confusing because it flips the inequality, but mathematically it says the same thing. However, for clarity, it is often better to write the inequality in the form where \(x\) is on the left side, showing more directly what \(x\) must be or exceed. 

Do you want details on how to solve this inequality or have any other questions?

**Related Questions:**
1. How would you solve the inequality \( 231 + 18x \geq 510 \) for \(x\)?
2. What is the significance of using inequalities in real-life scenarios like this one?
3. Could you explain how changing the number of glasses per set would affect the inequality?
4. What would be the new inequality if the restaurant already had 300 glasses?
5. How can inequalities help in planning and inventory management?

**Tip:** Always ensure your inequalities are written to clearly show the variable you are solving for, as it can reduce errors and confusion in interpretation.

Isabella needs to order some new supplies for the restaurant where she works. The restaurant needs at least 510 glasses. There are currently 231 glasses. If each set on sale contains 18 glasses, which inequality can be used to determine x, the minimum number of sets of glasses Isabella should buy?

Learn how to solve the inequality for determining the minimum number of sets of glasses required when a restaurant needs at least 510 glasses, and there are currently 231 glasses. This problem covers core algebraic concepts and properties of inequalities. Suitable for students in Grades 6-8.

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