Drain and vent for laundry tub

I need some help with draining and venting a laundry tub in my basement. The 3"drain line runs horizontally right behind where the sink is to be installed. The stack is on the other side of the room so I am not sure how to pipe this properly. Can I use an AAV?

I have some "homeowner" plumbing experience so the actual piping I can do, I am just not up on the codes and proper venting.

any help would be appreciated.

You have the right idea. We can not use AAV's here so you would have to run the vent through the roof or tie into another vent, but, if AAV are acceptable in you area, you're good to go. Of course, if it's not getting inspected, you're the only one who has to live with it.