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