I have noticed that people who use these mechanical algorithms for problems of this sort often end up with the wrong answer. I'm sure that the formulas work if they are used correctly, but in practice they seem to invite arithmetic mistakes. So I prefer to avoid the formulas and use more common-sense methods.

In this case, if you can deal with the first three congruences then you know that , and you want to combine this with . The first of those congruences looks simpler if you add 7 to both sides, to get . By good fortune, the second congruence also looks simpler if you add 7 to both sides, to get . So x+7 is a multiple of both 11 and 30, and therefore it is a multiple of 330. Therefore .