Question

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 $15,000. The price of car A is $130,645. a. Assuming that you do not know which model is more expensive, write an absolute value in equality that describes this situation. Use x for the cost of car B. b. What are the possibilities for the price of car B?

Write an absolute value inequality that describes the given situation?
A) x can be any value between $115,645 and $145,645.
B) x must be less than $115,645.
C) x must be greater than $145,645.
D) x can be any value except $130,645.

Answer 1

The absolute value inequality representing the situation is |x - 130645| > 15000, leading to the conclusion that the price of car B must either be less than $115,645 or greater than $145,645.

Step-by-step explanation:

When tasked with determining the cost of car B given that its price differs by more than $15,000 from car A, which costs $130,645, we can express this situation using an absolute value inequality. The inequality will describe the possible values of x, where x represents the price of car B. To incorporate the given condition that the difference in prices exceeds $15,000, the absolute value inequality is written as |x - 130645| > 15000.

To find the possibilities for the price of car B, we can solve the inequality in two cases:

• Case 1: If x is greater than $130,645, the inequality becomes x - 130645 > 15000, which simplifies to x > 145,645.
• Case 2: If x is less than $130,645, the inequality becomes -(x - 130645) > 15000, which simplifies to x < 115,645.

Therefore, the prices for car B must either be greater than $145,645 or less than $115,645. This information aligns with option B (x must be less than $115,645) and option C (x must be greater than $145,645), but not with option A or D, making options B and C collectively the correct answer. Car B cannot cost between $115,645 and $145,645, and it certainly cannot be exactly $130,645 (since the difference must be more than $15,000).