I just bought this used 2003 Honda Accord with 82000 miles on it from Arizona, as I have no knowledge about cars, I was wondering if it would be safe to go on a long trip.
My car has 82000 miles.
My car has an automatic transmission.
Ultimately, you are the only one that can make that decision. I would suggest having a mechanic do a vehicle inspection before setting out on a long trip like this, as 3000 miles will pass some maintenance milestones. Having an inspection done before you set off should be able to identify any major issues that loom, and will give you a chance to get them repaired, which will at least lessen the likelihood of a breakdown. An inspection should cover belt status, major leaks, brake condition, hose health, fluid condition, and most of the overall condition of the vehicle. If this is something that you would like to have done, contact a certified mechanic, like those available at YourMechanic.com.
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