Physics Concept Question Help!?

Newtons first law states that objects remain at rest or in uniform motion provided no external unbalance force acts on them. Newtons third law states that a force always occurs in pairs - the two force of a given pair acting will equal strength and in opposite direction. Doesn't Newtons third law imply that force are always balanced? If so, it would never be possible for anything to accelerate. By witting a specific example, illustrate how this apparent paradox can be resolved.