Example

Suppose x Z + Zi, the ring of Gaussian integers, is a solution of the equation

(2 + i)x = 5.

Then, by the cancellation law, the equation is equivalent to the one obtained by left multiplication with (2 - i) on both sides:

5x = 5(2 - i).

Applying the cancellation law once more, we find

x = 2 - i.