In general dumbbells are thought to be the better way to train. Many beginners do not use dumbbells. Why? Because they don't know how. A session or two with a trainer will be all that is needed. The dumbbell area in a gym looks intimidating. Much of that intimidation is just because you don't know what to do and you'll feel like you look silly. Don't worry! We all started there.
You may want to read Weight training Part 1
Having said that when you are new to a gym you will be shown the machines only. There really is no problem with doing machines for awhile. The reason dumbbells are better is because each arm has to work. For example, if you are using a biceps curl machine and you are right handed, your right hand can compensate for your left hand and you either may not know it is happening or you just let it happen.
Using a dumbbell in each hand makes it impossible to "cheat." Each hand has to lift the weight on its own. Again having said that there is less risk of injury if you use a machine versus using the wrong form with dumbbells. So learn the correct form. For example using the biceps curl you want to lift with your muscles and not momentum - thus you back should not be helping you lift the weights.
Perhaps the best advice is to switch your workout around. One month use machines; one month use dumbbells. Or use dumbbells for your biceps but go over to the triceps machine to work that area. Of course a good plug for dumbbells is that you can workout at home.
A note about barbells: you will find that although the use of barbells are great training devices you can compensate very easily so be aware of that. For example, if you are at home doing a chest press with a barbell make sure both arms are working evenly to lift the bar.
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