Select the most appropriate option that can substitute the underlined segment in the given sentence.
Last night, I failed to sleep because of some familiar issues that couldn’t be avoided.

The correct answer is inevitable.

Let's analyze the underlined segment in the sentence: "some familiar issues that couldn't be avoided."
We need to find a single word from the options that has the same meaning as "that couldn't be avoided" (something that is impossible to avoid or prevent).

Let's evaluate the given options:
1. unthinkable: impossible to imagine or accept; extremely unlikely.
2. unsolvable: impossible to solve or find an answer to.
3. inevitable: certain to happen; unavoidable. This perfectly matches the meaning of "couldn't be avoided."
4. incapable: lacking the ability or strength to do something.

Therefore, the word inevitable is the most appropriate substitute for the underlined segment.