Translation:I am not busy this week.
This seems odd. I'm used to seeing and saying 「〜忙しくないです。」 Instead of 「〜忙しくありません。」
Very much so. I definitely don't like not conjugating the adjective; it's certainly not typical Japanese, even if it is actually understood.
Ohhhh, I get it! You're just replacing the -nai in "kunai" with "arimasen".
Was it too hard to put in 忙しくありません with the kanji? Seriously, I have NO CLUE how they'll do a mandarin course if they continue to avoid kanji / hanzi like it's the plague.
Meaning they use it regularly, and if you want to read Japanese you should learn it too. What is this course, "hiragana nihongo" for little kids? We're barely learning any new kanji. The earlier we start learning verb kanji, the better.
Normally I see sentences like this as being capable of both present and future tense (I am going/I will go, I am studying/I will study, things like that) but on this sentence I wrote "I will not be busy this week" and it was counted as wrong. Can someone help explain?
You use “dewa arimasen” with nouns, but you have to use “arimasen” with -i adjectives.
Should it not be : 今週はいそしいじゃありません。OR 今週はいそがしくないです。？ 今週はいそがかしくありません。 seems very odd indeed.
You can't use "ja arimasen" with -i adjectives, but the second would be correct, 今週はいそがしくないです。 There's nothing wrong with "arimasen", but "nai desu" is more common in speech.
If arimasen is used for inanimate objects, wouldn't "imasen" be used here since it's talking about yourself? Or since "arimasen" translates to "there is not" would it literally translate to "there is not business this week"?
You should think of "arimasen" as having a different grammatical function when used with adjectives.
帽子がありません。 Boushi ga arimasen. There is no hat.
忙しくありません。 Isogashiku arimasen. I am not busy.
In the second sentence, "arimasen" is making the adjective negative. You can think of it as a negative version of the verb "to be" that is used with -i adjectives.
"Ja arimasen" serves the same function with nouns and -na adjectives.
男じゃありません。 Otoko ja arimasen. I am not a man.
きれいじゃありません。 Kirei ja arimasen. I am not pretty.
In meaning, no.
"Arimasen" is a little more polite, but "nai desu" is more common in speech.