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

Given 2 numbers, a and b. The number exactly in the middle of a and b is $\displaystyle{ \frac{a+b}{2}}$.

For example, the number exactly in the middle of numbers 5 and 17 is (5+17)/2=22/2=11.

Check: 11-5=6, 17-11=6



The number in the middle of 24 and 92 is (92+24)/2=116/2=58.

The positive difference between 58 and both 24 and 92 is :

58-24 = 34     &    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

so     x≤58+34                 or                    -x≤34-58

             x≤92                   or                    -x≤-24, that is x≥24



Answer:      |x-58|≤34 ;   24≤x≤92