Question

The shortest person in a class is 55 inches tall and tallest person in that class is 75 inches tall. Write an absolute value equation that represents the minimum and maximum heights. Use x to represent the heights.

Answer 1

Answer:

$|x-65|\leq 10$

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

$Midpoint =\frac{Maximum+Minimum}{2}=\frac{75+55}{2}\Rightarrow \frac{130}{2}=65$

Difference between extreme points and midpoint is

$Difference =\frac{Maximum-Minimum}{2}=\frac{75-55}{2}\Rightarrow \frac{20}{2}=10$

The absolute value equation is

$| x - Midpoint | \leq Difference$

$| x -65 | \leq 10$

Therefore the required absolute value equation that represents the minimum and maximum heights is |x-65| ≤ 10.

Answer 2

x = minimum

<x+25 maximum

x=55