Давайте заменим модальные глаголы в предложениях их эквивалентами:
1) He couldn't explain anything — He was not able to explain anything.
2) You must not stay here — You are not allowed to stay here.
3) Can you swim? — Are you able to swim?
4) You may take these books — You are permitted to take these books.
5) They can run quickly — They are able to run quickly.
6) She might work in our room — It is possible that she will work in our room.
7) Who can read this text? — Who is able to read this text?
8) They must go there tomorrow — It is necessary for them to go there tomorrow.
9) May I go to the cinema? — Is it possible for me to go to the cinema?
10) We must meet at 7 o'clock — It is necessary for us to meet at 7 o'clock.
Эти эквиваленты помогают избежать модальных глаголов, используя другие конструкции для выражения возможности, способности, разрешения или необходимости.