Consider a set L consisting of n lines in the plane. No two of them are parallel but many can pass through a single point. By drawing these lines we create vertices (intersection points of the lines), edges (parts of the lines between intersections and semiinfinite rays extending from the first and last intersections on a line to infinity), and faces (connected parts of the plane after removing the lines from it).Prove that unless all the lines pass through a single point, there exist at most n faces bounded by 2 (semiinfinite) edges.
I have completed this proof in another way. But apparently, I am supposed to get a result that involves this expression, $e \ge 3f - n $. I have no idea where this inequality comes up in the proof nor how to use it. I got the inequality as a hint from the book. Thank you in advance.