Proving "3f ≤ 2e" for Planar Graphs

[kinof]

Homework Statement

Prove that for a simple, connected, planar graph, 3f ≤ 2e where f = faces and e = edges

The Attempt at a Solution

My professor went over this in class, and mentioned something about "double counting," which I do not really understand. I tried saying that it takes 2 counts to define an edge and 3 to define a face, but from here I am not sure what to do as I am unfamiliar with double-counting proofs.

Thanks for the help.

 

[tiny-tim]

hi kinof!

My professor went over this in class, and mentioned something about "double counting,"

every edge has exactly two faces, so slice every edge in two, lengthwise …

then you have double the number of edges, and every edge has only one face