The best explanation for the observation of the balloon moving backward relative to the car when the car starts moving forward is:
The car moves forward, while inertia keeps the balloon in place.
This statement accurately describes the effect of inertia, which is the property of an object to resist changes to its state of motion. When the car accelerates, the balloon tends to remain in its original position due to inertia, making it look like it is moving backward relative to the car.