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Basically if K is less than 10^3, meaning that the acid/base barely disassociates, then we can assume that the dissociation affects the initial condition of your acid/base so little that it's insignificant. This means that when calculating your x, or the change in concentration, instead of have your denominator being [inital] - x, you can just leave it as [initial] since the concentration does not change significantly.
It's also important to double check that the x value is in fact less than 5% of the initial concentration or the approximation is invalid. I always do that at the end of every problem in which I approximate, especially when the K value is only slightly smaller than 10-3