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How are tattoos viewed at both law school and in the legal profession? I figure that because I'll be wearing long sleeve shirts I should be able to cover them up. Will that be a problem with schools or employers?

If you keep them covered, no.

If they're covered by sleeves how they even going to know? Personally, I have ink and no one in my office knows I have any tats because none of them are on my neck/wrists/hands