The average size 8 shoe is approximately 8 1/2 inches plus or minus a quarter of an inch . Write and solve an absolute value inequality that shows the range of possible lengths of a person'a foot that would wear a size 8.
To solve this problem, we can start by defining the range of possible lengths of a person's foot for a size 8 shoe.
According to the given information, the average size 8 shoe is approximately 8 1/2 inches plus or minus a quarter of an inch. This means that the shoe size could be between 8 1/2 + 1/4 inches and 8 1/2 - 1/4 inches.
Let's call the length of a person's foot "x". To express the range of possible lengths, we use an absolute value inequality. The absolute value of the difference between "x" and the average size 8 shoe length should be less than or equal to the tolerance of plus or minus a quarter of an inch.
The inequality can be written as:
| x - 8 1/2 | ≤ 1/4
To solve this inequality, we can split it into two cases based on the inequality symbol inside the absolute value symbol.
First, when x - 8 1/2 is positive or equal to 1/4:
x - 8 1/2 ≤ 1/4
Adding 8 1/2 to both sides, we get:
x ≤ 8 1/2 + 1/4
x ≤ 8 3/4
Second, when x - 8 1/2 is negative or equal to -1/4:
-(x - 8 1/2) ≤ 1/4
Simplifying the inequality:
-x + 8 1/2 ≤ 1/4
Adding x and subtracting 8 1/2 from both sides, we get:
x ≥ 8 1/2 - 1/4
x ≥ 8 1/4
Therefore, the absolute value inequality that shows the range of possible lengths of a person's foot for a size 8 shoe is:
8 1/4 ≤ x ≤ 8 3/4