The advice given in this thread has been top notch, so I'd just like to add a couple of extra items. When you board the plane, let the flight attendant know you're nervous. They may also help you to relax too. Also LAX is a fantastic airport. It's big but so well marked, and easy to get around. I found it to be one of the best airports I've flown in and out of. Well marked, the people are VERY friendly there, and easy to navigate. It's big, however, so you'll get some major steps in that day. I've flown a dozen or so times by myself. I kind of prefer it, as I can just listen to some music in peace to myself while flying. Even if the flight is a little bumpy, the music makes it a breeze.
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