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.
If x is the foot length,
|x-8.5| <= .25
Let's define the variable "x" as the length of a person's foot.
According to the information given, the average size 8 shoe is approximately 8 1/2 inches, with a possible deviation of a quarter-inch in either direction.
To represent the length of a person's foot that would wear a size 8, we can write the absolute value inequality:
|x - 8.5| ≤ 0.25
Now, let's solve the inequality:
To remove the absolute value, we can split the inequality into two cases:
1. x - 8.5 ≤ 0.25
2. x - 8.5 ≥ -0.25
Case 1:
x - 8.5 ≤ 0.25
x ≤ 0.25 + 8.5
x ≤ 8.75
Case 2:
x - 8.5 ≥ -0.25
x ≥ -0.25 + 8.5
x ≥ 8.25
Therefore, the range of possible lengths of a person's foot that would wear a size 8 is 8.25 ≤ x ≤ 8.75 inches.
To write and solve an absolute value inequality that represents the range of possible foot lengths for a size 8 shoe, we can use the information given - 8 1/2 inches plus or minus a quarter of an inch.
Let's define the variable x as the foot length in inches. The absolute value of x minus the average foot length for a size 8 shoe, 8 1/2 inches, should be less than or equal to a quarter of an inch:
| x - 8.5 | ≤ 0.25
This inequality ensures that the difference between the foot length and the average foot length doesn't exceed a quarter of an inch.
To solve this absolute value inequality, we need to isolate the variable x on one side of the inequality sign. Let's consider two cases:
Case 1: x - 8.5 ≥ 0 (Positive case)
In this case, the absolute value | x - 8.5 | simplifies to x - 8.5. So, we have:
x - 8.5 ≤ 0.25
Solving for x:
x ≤ 0.25 + 8.5
x ≤ 8.75
Case 2: - (x - 8.5) ≥ 0 (Negative case)
In this case, the absolute value | x - 8.5 | simplifies to -(x - 8.5), which is the opposite of x - 8.5. So, we have:
-(x - 8.5) ≤ 0.25
Solving for x:
-x + 8.5 ≤ 0.25
8.5 - x ≤ 0.25
To isolate x, subtract 8.5 from both sides:
-x ≤ 0.25 - 8.5
-x ≤ -8.25
Remember, when multiplying or dividing by a negative number, we need to reverse the inequality sign:
x ≥ 8.25
Thus, the solution to the absolute value inequality is x ≤ 8.75 (non-negative case) or x ≥ 8.25 (negative case). Combining these inequalities, we can represent the range of possible foot lengths for a size 8 shoe as:
8.25 ≤ x ≤ 8.75