| x/5-8 |=3 means x/5-8=3 and 8-x/5=3.
That means x=55 or x=25 by solving each for x.
No other values of x make the equality true. Intervals apply for inequalities not equalities.
If we replace = with ≤ we get x≤55 and x≥25 and the interval is [25,55].
This is the result in interval notation for solving | x/5-8 |≤3.