"Я не можу працювати без інтернету."
Translation:I cannot work without the internet.
From Oxford dictionaries (http://www.oxforddictionaries.com/words/cannot-or-can-not):
Both cannot and can not are acceptable spellings, but the first is much more usual. You would use can not when the ‘not’ forms part of another construction such as ‘not only’. For example:
These green industries can not only create more jobs, but also promote sustainable development of the land.
The sentences with cannot are mostly accepted in this course but always marked as an error. Has it been decided on purpose? - Reported in case it's a mistake or just left out from the correct answers.