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

x = minimum

<x+25 maximum

x=55

Answer 2

`|x-65|\leq 10`

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 =(Maximum+Minimum)/(2)=(75+55)/(2)\Rightarrow (130)/(2)=65`

Difference between extreme points and midpoint is

`Difference =(Maximum-Minimum)/(2)=(75-55)/(2)\Rightarrow (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.