Highway patrol officer X stopped a vehicle on the freeway for speeding. Prior to issuing a ticket for speeding, Officer X looked around the car and asked the driver to open the glove compartment. The driver voluntarily complied. Drugs were found in the glove compartment. Officer X then arrested the driver and searched the whole car, including a briefcase marked "private" that was found in the trunk of the car.
Was the search of the trunk valid?
Was the search of the briefcase valid? Justify your answers.