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When the K value is less than 10^-3, it is safe to assume that the value of x will be negligible compared to the initial concentration. However, to make sure that x can be excluded from the denominator in the K expression, you can check that x is less that 5% of the initial concentration.
this is correct, it's basically just used to save yourself time not doing the quadratic equation and assuming that a small value being subtracted in the denominator won't really change the equation. because we say it's negligible and not that it's zero, we still keep the x squared in the numerator
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