Should i buy a 1997 infinity I30 that has about 160,000 miles on it thats in good condition for $3,000 and will it brake down on me with those kind of miles?

Look up the VIN on CarFax.com. Have a mechanic look at it to
see how well it has been taken care of. Being an Infiniti, there's
a good chance that is was, but you never know.

Look up the value on Edmunds.com and see if you're getting a
good value. For $3,000, that's a pretty good price off the top of
my head, but try to make sure no major work is needed on it or
your $3,000 car could become a $6,000-$7,000 car quite quick-
ly if a major repair (e.g. transmission replacement, etc.) will be
needed shortly. If you're worried about repair expense, I would
suggest a more frugal car like a Honda or Toyota with about 10
thousand miles per year of use.
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Depends on body condition.