problem: Suppose $2a-3b = -23$. Given that $a$ and $b$ are consecutive integers, and $a<b$, what is the value of $a$?
solution: Note that $b = a+1$. Substituting, we obtain $2a-3(a+1) = -23$. Note that $2a-3(a+1) = 2a-3a-3 = -a-3$. Since $-a-3 = -23$, we have that $a = \boxed{20}$.