# Need help understanding algebra steps taken in proof of why an even minus an odd is odd

I don't understand the algebra used in the below example proof from my textbook. Where does the + 1 come from? Is it okay to just add 1 anywhere you want? Or is there some rule here or reason you can?

• $2r - 2s - 1 = 2r - 2s - 2 + 1 = 2(r - s - 1) + 1$ – Artem Mavrin Apr 25 '16 at 4:16

$$2r-2s-1=2r-2s-1-1+1=2r-2s-2+1=2(r-s-1)+1$$