Answer:
Part a:
Price of car A = $131,745 and price of car B is unknown = x
There are two possible cases: 1) Car A is the more expensive car, and 2) car B is the more expensive one. We start by analyzing both cases separately:
Case 1) If car A is the more expensive car, we could write the difference in prices in mathematical form, using the "larger than" symbol: ">"
$131,745 - x > $15,000 that reads :"the price of car A ($131,745) minus the price of car B (x) is MORE THAN (>) $15,000
Case 2) Car B is more expensive than A, so we can write:
x - $131,745 > $15,000 that reads: "the price of car B (x) minus the price of car A ($131,745) is MORE THAN (>) $15,000
Both inequalities that we wrote above can be condense in a single inequality if we use the "absolute value" mathematical symbol thus expressing that the difference between both prices in absolute value must be larger than $15,000:
| $131,745 - x | > $15,000
Part b) We can solve for x in the first inequality we wrote:
$131,745 - $15,000 > x therefore x < $116,745
and also we can solve for x in the second inequality given us the second possibility:
x - $131,745 > $15,000 therefore x > $146,745
