Question

The shortest known adult woman is about 24 inches tall and tallest known adult woman is about 92 inches tall. Write an absolute value equation that represents the minimum and maximum heights. Use x to represent the heights.

Answer 1

24inch[less than and equal to sign]x[less than and equal to sign]92inch

Answer 2

An absolute value equation that represents the minimum and maximum heights 24 ≤ x ≤ 92.

Explanation:

First we have to know about the middle number. The middle number between 24 and 92 is :

`\frac {(24+92)}{2}= 58.`

Now positive difference is: 58-24=34 and 92-58=34.

Thus the height of a woman x, can vary at most 34, from 58. That is the height of a woman can be 34 ft less or more than 58.

In absolute value notation this is expressed as:

x-58≤34

what this means is that:

x-58≤34 or 58-x≤34

Further solving the equation gives: |x-58|≤34 ;

24≤x≤92