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The problem provides the following information:

- Most insurance companies replace a vehicle when the repair costs exceed 80% of the car's "blue book" value.
- Michelle's insurance company paid $7,500 for repairs.

Let the blue book value of Michelle's car be denoted as $ x $.

The insurance will replace the car if the repair cost exceeds 80% of $ x $. Mathematically, this means:
\[
7500 \leq 0.8x
\]
Now, we solve this inequality to find a conclusion about $ x $.

### Solution:
\[
7500 \leq 0.8x
\]
To solve for $ x $, divide both sides by 0.8:
\[
x \geq \frac{7500}{0.8}
\]
\[
x \geq 9375
\]

This means the blue book value of Michelle's car must be at least $9,375.

Would you like more details on any part of the solution?

Here are 5 related questions to expand your understanding:
1. What happens if the repair cost exceeds 100% of the blue book value?
2. How do insurance companies use blue book values in other cases?
3. Can the blue book value of a car change over time?
4. What other factors influence insurance payout decisions for car repairs?
5. How is the blue book value of a car calculated?

**Tip:** Understanding inequalities and their real-life applications helps in solving a wide range of problems, from finance to engineering.

Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of the 'blue-book' value of the vehicle. Michelle's insurance company paid $7,500 for repairs on her car after an accident. What can be concluded about the blue-book value of the car?

Learn how to solve an inequality to determine the blue-book value of Michelle's car. The problem involves calculating the minimum blue-book value based on a repair cost of $7,500, which is 80% of the car's value. Perfect for students in Grades 6-8.

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