Answer:
[tex]|x-65|\leq 10[/tex]
Step-by-step explanation:
It is given that the shortest person in a class is 55 inches tall and tallest person in that class is 75 inches tall.
Let x represent the heights.
Minimum value of x = 55
Maximum value of x = 75
The midpoint of maximum and minimum value is
[tex]Midpoint =\frac{Maximum+Minimum}{2}=\frac{75+55}{2}\Rightarrow \frac{130}{2}=65[/tex]
Difference between extreme points and midpoint is
[tex]Difference =\frac{Maximum-Minimum}{2}=\frac{75-55}{2}\Rightarrow \frac{20}{2}=10[/tex]
The absolute value equation is
[tex]| x - Midpoint | \leq Difference[/tex]
[tex]| x -65 | \leq 10[/tex]
Therefore the required absolute value equation that represents the minimum and maximum heights is |x-65| ≤ 10.
