Given ma+ mb=mb + mc prove mc= ma write a paragraph proof to prove the statement

As a property of equations, you can add or subtract the same quantity to/from both sides, and the truth value of the equality will remain the same: if you start with something true, e.g. 7=7 and add the same quantity to both sides, e.g. 7+4=7+4, you will still have something true, i.e. 11=11.

On the other hand, if you start with something false, e.g. 3=7 and add the same quantity to both sides, e.g. 3+6=7+6, you will still have something false, i.e. 9=13.

So, you can subtract from both sides to transform the equality into

as required.