left arm weaker

i read about the size difference in arms, my problem is basically my left upper body is weaker than my right, but my right lower body is weaker than my left. as of right now i stop my right reps on dumbells at what ever number my left failed at.should i keep going on my right and then just do an extra set or 2 on my left to make up the difference.need some advice here guys thnx.