1. An object at rest will remain at rest. This is known as Newton's First Law of Motion, or the law of inertia. If all the forces acting on an object cancel each other out, the object will not accelerate.
2. An object in motion will continue moving at a constant velocity. This is also part of Newton's First Law. If the forces are balanced, there's no net force to change the object's speed or direction, so it will continue moving at the same speed and in the same direction.