Most vehicles need a couple drive cycles for all the monitors to report to the ECM that everything is in good working order. A drive cycle consists of a cold start (sitting overnite), turning on electrical accessories (heater or AC, lights, etc) some city driving and some highway driving. Depending on the vehicle and your driving habits it could take several cycles.
Drive the vehicle for 5 full driving cycles and if the light stays off you are ok and can pass inspection.
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Before a long drive you have to bring the car to your mechanic for an inspection and a check up. He'll suggest you what should be fixed before you go for a long distance drive.