Find an integer $x$ such that $-2310\leq x\leq 2310$ and
$x \equiv 1 $ (mod 21) $x \equiv 2 $ (mod 20) $x \equiv 3 $ (mod 11)
I think I have a solution but was is confusing me is that $x$ has to be $-2310\leq x\leq 2310$. So, it's only saying that $x$ has to lie between those bounds and my modulus does not. My work is as follows:
You are right! Your work shows that there exist an infinite number of x that satisfy your system of congruences, but only one of them lies in the indicated range.