I have been given the following assignment:
Charles is rich or clever.
If Charles was clever, he'd have a job.
But, Charles doesn't have a job, so he must be rich.
The translation I gave (verified by the book) is:
r = rich, c = clever, j = job
r OR c, c IMPLIES j, NOT j ENTAIL r
which translates to:
r OR c 1.
c IMPLIES j 2.
NOT j 3.
The book gives a rather elaborate solution.
Why can't I just:
r 4. OR-ELIMINATION of 1
?
You can't immediately deduce $r$ because the first premise isn't a conjunction; it's a disjunction $$r \lor c\tag{1}$$ and so you can't invoke $\land$-elimination to conclude $r$ from premise $(1)$.
Edit:
You've misunderstood what $\lor$-elimination involves and/or requires. It certainly does not license you to conclude either $r$ or $c$ from $r\lor c$ alone. What happens if $r = F$ and $c = T$? In that case, $r\lor c$ is true, because $c$ is true. So concluding $r$ from $r\lor c\,$ is, in fact, a fallacy. All you know is that one, or perhaps both, disjuncts hold.
Instead, you can assume $r$, which immediately implies $r$, and then assume $c$ from which you'll be able to deduce $r$, and then by $\lor$-elimination, conclude therefore $r$.