The question wants $x < 7$ and $x < 13$.  Between these two requirements, $x < 7$ is more restrictive.  In other words, for all $x$ values that are less than $7$, they are already also less than $13$.  Therefore the requirement that $x < 7$ already covers $x < 13$, and the two requirements can be combined into just $x < 7$.  So the answer is $B$, $(-\infty, 7)$.