Answer
Yes, x is rational. $x = \frac{d-b}{a-c}$
Work Step by Step
Expanding, we get $ax+b = cx+d, ax-cx = d-b, (a-c)x = d-b, x = \frac{d-b}{a-c}$. Since $a,b,c,d$ are all integers, $x$ is the ratio of an integer to another integer, so it must be rational, so the statement is proven.
