Answer
See the explanation
Work Step by Step
The minimum weight allowed was 62 kg and the maximum weight allowed is 72 kg.
The absolute value equation will be of the format $$| x - h | = d,$$ where $d$ is the distance from halfway point to $max$ or $min$ value and $h$ is the halfway point between the min and max values in the number line.
If the solutions are $62$ and $72$, then $max=72$, $min=62$ and the distance $d$ is obtained as $$d = 0.5 * (max - min)= 0.5 * (72 - 62) = 5.$$ The halfway point $h$ is $$h = min + d= 62 + 5 = 67.$$ Substituting in the first equation, the absolute value equation that represents the minimum and maximum distances is $$ |x - 67 | = 5.$$
A real-life example is the following:
A factory machine operates best when the temperature is $67°$C, but it can still run if the temperature is within $5°$C of that. What are the minimum and maximum allowed temperatures?
