How can I find an unknown "x" in a mod problem? Ex: 18 = x(mod 4) I should point out that the "=" has 3 lines

Answer 1

The easiest way is to divide the mod into the number
as 18 divided by 4 = 4 remainder 2.
Normally we are more interested in the quotient than the remainder but in MODS we want the remainder so
18 = 2 mod 4
19 = 3 mod 4
20 = 0 mod 4
21 = 1 mod 4
22 = 2 mod 4
notice these MOD classes are always less than the mod #

Answer 2

For the problem "Find all x such that x is congruent to C (mod 4)", for a constant C, there are only four possible answers, namely:

{4k, k any integer} = {all x such that x is congruent to 0 mod 4}
{4k+1 ... } = { all x such that x is congruent to 1 mod 4}
and similarly for 2 and 3.

In this case, 18 is congruent to 2 mod 4, because in particular it equals 2 + 4*4. So the answer is the set of all x such that x is congruent to 2 (mod 4), or whatever notation your teacher prefers for the concept.