What is the inversion operation of this problem. z-8=91/3

It is a good idea to look at the operations performed on the variable from the point of view of order of operations. Here, the value 8 is subtracted from z.

Addition is the inverse operation of subtraction. To undo the subtraction of 8, you must add 8.


Of course, anything you do to one side of the equation must also be done to the other side. That's what keeps the sides equal.
.. z -8 +8 = 91/3 +8
.. z = (91 +24)/3
.. z = 115/3