@emma-xx,
It's possible.
Just start with the probability that X is less than or equal to x, and then subtract the probability that X equals x. You get the probability that X is less than x.
P(X < x) = P(X is less than or equal to x) - P(X = x).
Whenever you have two mutually exclusive events, A and B, then P(A) = P(A or B) - P(B).