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If it's a sleeve on your arm you'll be fine. Most employers are only concerned about tattoos you can't cover, ie. on your hands or neck/face. I have both my forearms tattooed and have never had trouble getting a job. Well, I have, but it wasn't because of the ink... just keep them under long sleeves for the interview and don't mention them unless you're asked. If they make a big deal of it and you have to wear short sleeves a lot, I read about a product called Dermablend which you can use to cover them up.
I agree, I've had a bunch of customer service jobs, some for big corporations, some for fine restaurants and I've got a band on my forearm and wrist. Just wear long sleeves and once they're hired you, it's GENERALLY considered discrimination if they try to get rid of you because of them afterwards, unless there is something written in their policy about appearance, in which case you have the option of wearing lon sleeves, or covering them with a bandana, or something like that if it isn't against uniform policies.