Two of the ten most expensive cars in the world are the BMW Z8 and the Mercedes Benz CL 600. The prices of these two cars differ by more than $10,000. The price of the Z8 is $130,645.
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 the CL 600.
b) What are the possibilities for the price of the CL 600?
a) To write an absolute value inequality that describes the situation, we need to express the difference in price between the two cars.
Let's assume x represents the price of the CL 600. The difference between the prices can be found by taking the absolute value of the difference between the two prices, which we will denote by |x - 130,645|.
The given information states that the difference in price is more than $10,000. We can express this as follows:
|x - 130,645| > $10,000
b) To determine the possibilities for the price of the CL 600, we can solve the absolute value inequality.
First, we can split the inequality into two separate inequalities:
x - 130,645 > 10,000 or x - 130,645 < -10,000
Solving the first inequality:
x - 130,645 > 10,000
x > 10,000 + 130,645
x > 140,645
Solving the second inequality:
x - 130,645 < -10,000
x < -10,000 + 130,645
x < 120,645
Therefore, the possibilities for the price of the CL 600 are x > 140,645 or x < 120,645.