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He's implying that when you have an extremely large quantity of something, and if you take an almost negligible amount from it, you basically still have the same amount you started with. That's why for some of the acid/base problems you can assume that "X" is 0, because if it's such a small number and you subtract it from a large one, you will basically end up with the same large amount.
Generally you would find the solution first assuming that x is negligible (less than 5% of your initial concentration), then see if the answer is actually less than 5% of whatever concentration you started out with. If it is, then your solution is viable; if not, you would have to redo the question with the quadratic formula. It's basically a "shortcut" to solve the problem without having to use the quadratic equation.
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