The $92,000 average value, and $22,000 actual value difference gives the the absolute value inequality that represent the range of values for the vintage cars at the car show and price range as follows;
(a) |92,000 - x| ≤ 22,000
(b) 70,000 ≤ x ≤ 114,000
What is the absolute value inequality that gives the price range?
Average value of the car = $92,000
Amount actual value of car could differ = $22,000
(a) An absolute value inequality has both inequality operators and absolute functions.
The absolute value inequality that represent the situation can be presented as follows;
Where;
x = The possible values of the vintage car
(b) Solving the absolute value inequality gives;
|92,000 - x| ≤ 22,000
or
|x - 92,000| ≤ 22,000
Which gives;
92,000 - 22,000 ≤ x ≤ 92,000 + 22,000
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