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 write and solve an absolute value inequality that represents the range of possible lengths of a person's foot that would wear a size 8 shoe, we can start by considering the given information.
The average size 8 shoe is approximately 8 1/2 inches, and it can vary by plus or minus a quarter of an inch. This means that the actual length of a person's foot can be 8 1/2 inches minus a quarter of an inch, or 8 1/2 inches plus a quarter of an inch.
Let's assign a variable to represent the length of the foot. Let's use x to represent the foot length.
The absolute value inequality that represents the range of possible foot lengths for someone wearing a size 8 shoe can be written as:
| x - 8 1/2 | ≤ 1/4
To solve this absolute value inequality, we'll break it into two separate inequalities:
1. x - 8 1/2 ≤ 1/4
2. - (x - 8 1/2) ≤ 1/4
Simplifying each inequality:
1. x - 8 1/2 ≤ 1/4
Subtract 8 1/2 from both sides:
x ≤ 1/4 + 8 1/2
x ≤ 8 3/4
2. - (x - 8 1/2) ≤ 1/4
Distribute the negative sign:
-x + 8 1/2 ≤ 1/4
Subtract 8 1/2 from both sides:
-x ≤ 1/4 - 8 1/2
-x ≤ -8 1/4
Multiply both sides by -1 (since we're dividing by a negative):
x ≥ 8 1/4
Therefore, the range of possible foot lengths for someone wearing a size 8 shoe is:
8 1/4 ≤ x ≤ 8 3/4