Translation:I am not busy.
Why is 'drunk' given in all of these lessons as an option?? When do we get to actually learn it?!? feeling trolled
Here 忙 is not an adjective (like adjectives in English). Technically, you must use the suffix -的 to mark an attribute of an object. The following sentence is grammatically correct:
我不是忙的。(this is an very awkward expression, don't say this in real life)
The usage of 忙 itself is somehow similar to a verb. Thus 我不忙 is a correct expression. If you know Japanese and Korean, you'll see similar phenomena in these languages too.
不忙 is a composite word that is an adjective meaning "not busy". Similarly, you can say 我不好 to mean "I am not good", or 我不笨 to mean "I am not stupid"
Why should we learn slang Chinese if we do not even know well-written, grammatically correct structures? Try writing ain't in a CV or cover letter and you'll see the result.
@Raskol - by that logic the following should also be accepted - "I ain't not busy"; "I ain't doin nothing"; "I ain't not doin nothing"; "I'm chilling out"; "I ain't have nothing to do"... etc etc... and possibly dozens of other such "grammatical gems".. You can't expect the Duo app to focus its energy on figuring out these 101 answers; rather than creating good quality Chinese content. My 2 cents.