For all real numbers A, B and for when C does NOT equal 0, the equations:

A = B and AC = BC are equivalent to one another.

Each side can be multiplied by the same NONZERO number without changing the solution set.

For all real numbers A, B and C, the equations:

A = B and A + C = B + C are equivalent to one another.

The same number may be added to each side of an equation without altering the solution set.