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The -x was ignored because the value would have been so small that 0.1-x would be rounded to 0.1. If K is less than 10^-3, you generally ignore the -x and use the initial concentration without explicitly factoring in the change.
x was ignored in this case because K is less than 10^-3 so you know that x is going to be too small for it to make a difference in that case. You can test to see if this approximation is accurate as long as your final answer is less than 5% of the initial
This is called the X is small approximation. Relative to the initial concentration, the change is so small, less than 10^-3 smaller, so we can treat it as the same number before and after without significant change. This makes our math much, much easier.
If the given K is less than 10^-3, then you can use approximation, meaning that you can disregard the X because it is small enough that it would not profoundly impact your equilibrium expression.
when the K is less than 10^-3, the x subtracted. is going to make such a small difference it's acceptable and easier to just ignore it. Only ignore when it is addition or subtraction though, you should include it in multiplication or division I believe. If concentration. found is less than 5% of the initial concentration that also confirms it was ok to do the. approximation
The removal of the -x occurs because it is extremely small relative to the chemical equilibrium. We don’t say it is 0 because the numerator would be affected. We say it is small relative to the rest of the equilibrium allowing it to be ignored.
X value was ignored because the K value was so small, meaning the amount of product formed compared to the reactants was very small. This means that the amount of products (x) can technically be ignored as a change factor which is why you can eliminate it.
X was ignored because 0.10 is less than 10^-3, which means it is so small that it would not make a difference to decrease by X; therefore, you only use the 0.10 (think of Dr.Lavelle's example of the million dollars minus $10).
The x is ignored because it is such a small value, thus will not affect the answer extremely. When doing calculations with small x, make sure you do not just plug in 0, but rather emphasize that it is negligible not 0.
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