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Vibration and steering wheel jerk to the left

I have a 2006 Mazda 3 Hatchback. We recently had new tires put on and an alignment both were needed pretty bad. Before the work the car had a pretty bad vibration to begin with. After the car ran smooth for about a week and then my described it having a vibration and thought something fell off. We took it back to the shop and they checked it over and rebalanced the tires and suspected that maybe a weight or two fell off. The car ran fine again and then this past weekend I was driving and noticed that around 60-70 the car vibrated but not consistently, as it slowed from 70 to 60 it seemed to vibrate more. I also noticed around 25 that it had the vibration occasionally and could feel a slight jerking or tug to the left.

My guess is I have a broken or cracked motor mount since its not consistent at any speed. My reasoning is that at the lower as I accelerate the engine rpms are causing the jerking and as I slow down the decrease in rpms is causing the vibration.

Any thoughts?

Yup. Take it to a good chassis shop, tell them all the gory details, and have them give it a good look-see.
Your logic is excellent. But it could also be a worn tie rod end, a bad ball joint, or a number of other possibilities. The only way to tell is with the car on a rack.