While doing curls with dumbells, my left arm fails first while I feel like I can still do maybe 3 or 4 more with my right arm. What is the best way to get my left bicep caught up? Today when my left failed I stopped picked up a lighter dumbell and only curled with my left until it failed. Is this the propper way?

If nothing is wrong with your left bicep then just try doing more with your left bicep. I had the same problem and over a years time of work in the gym and my chiropractor working on me it has got my left almost as strong as my right. You may well have some scar tissue in your left bicep which means you need someone that knows what they are doing to massage that muscle really super hard and break that scar tissue up and do it over time. If you are really concerned check with a chiropractor. What mine does is he flattens the bicep muscle out completely and then runs his two thumbs up the muscle and it hurts like hell but it's helped my strength a lot. Also it's worth noting that if you are right handed it's common to have around 10% to 15% less strength in your left bicep but sounds to me like you have even less than that.

What you're doing is actually a very good way to get better symmetry. Sounds kind of like a drop set. If you don't see gains in a few weeks you might try to do a little extra work on the left, maybe on a different day.

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Keep your body lean, your blood clean and your mind sharp. -Rollins