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Part 1
Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than ​$10 comma 000. The price of car A is ​$131 comma 545.
a. Assuming that you do not know which model is more​ expensive, write an absolute value inequality that describes this situation. Use x for the price of car B.
b. What are the possibilities for the price of car​ B?

1 answer

To tackle this problem, let's break it down step by step.

Part 1a

We know the following:

  • The price of car A is $131,545.
  • The price difference between car A and car B is more than $10,000.

This leads us to write an absolute value inequality. The absolute value inequality that represents the situation can be set up as follows:

\[ |x - 131,545| > 10,000 \]

Here, \( x \) represents the price of car B.

Part 1b

To find the possibilities for the price of car B, we will solve the inequality \( |x - 131,545| > 10,000 \).

This inequality means that the price of car B (x) must either be more than $10,000 greater than the price of car A or more than $10,000 less than the price of car A.

  1. Case 1: \[ x - 131,545 > 10,000 \] \[ x > 141,545 \]

  2. Case 2: \[ x - 131,545 < -10,000 \] \[ x < 121,545 \]

Conclusion

Therefore, the possibilities for the price of car B \( x \) are:

\[ x < 121,545 \quad \text{or} \quad x > 141,545 \]

In summary:

  • The price of car B can be less than $121,545 or more than $141,545.