I've figured out that Now I want to set up the truth table, but I'm unsure how to do that when there are three variables instead of two. Can you help me?
With 3 inputs you have 8 different possibilities (2^3). Start from 000, then 001, then 010 and so on up to 111 (binary counting). Apply each possibility to your boolean equation and find X.
A'BC has to take an input of 011 as for the AND gate to output a 1. You need to have 0 logic for inverting inputs as to be taken as 1 from the AND gate.