In this case the right option is the first one, <em>Neither of the children had the inclination to clean their rooms</em>. The word <em>inclination</em> is derived as stated from the Latin <em>clinare </em>and it is formed by putting together in+clinare, "lean toward [in/into]". The opposite would be "decline", formed by joining de+clinare.
What do you mean LA do you mean the great state of louisiana?
Not a complete article, but:
Pros: You get places faster, more efficiently
Cons: Pollution, car crashes