Translation:Modern teenagers can not live without the Internet.
Please allow this answer, as "the internet" is also commonly just called "internet":
Modern teenagers can't live without internet.
If any Ukrainian speaking contributors and mods need to know why, it would be the same as saying "I can't live without cigarettes." Or, "I can't live without chocolate." The article the is not necessary. Internet, said on its own without the article is said often. (We wouldn't say "I can't live without the chocolate.")
Other example of how this is used:
"Do you have internet?"
"Does the hotel have internet?"
Anyway, thank you for considering! The default answer is acceptable in this sentence, but I would like to see my example added.
(The use of "the" is certainly used at times when we say something like "The internet is not working", or, "My dad has never used the internet.")