How do +damage mods work when dual wielding?

There are rings, shields and many other non-weapon items that give a small boost to damage. If someone wears say a ring with +3-5 dmg, and dual wields - does this mean that it will give the full effect to both weapons? Or only to the main weapon, split among them or some other variant?

Solution 1:

When dual-wielding, you hit alternating with your main and your off-hand weapon, receiving a 15% attack speed bonus. So in the end, you'll get half of that damage bonus if if you only have it on one of your weapons, but the full bonus if you have it on both or on any other accessory. But the end effect is that you get the average, as you also only hit with the average of your two weapons.

So you should in general only dual-wield with weapons that are very similar in damage, or you'll do less damage than you could with a sword and shield combination.