Q: My car makes a noise and vibrates when I put it in reverse. no problem forward on 2005 Chevrolet Malibu

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Purchased car 5 days ago with 138K.
(1) Answer
Possible motor mount problem. Set park brake and have a helper hold service brakes then shift to rev. & drive, engine running of course, while you observe engine movement, shouldn't be excessive! While in reverse, hold brakes and add slight throttle may help.

Assuming that it is not a trans. problem!