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He turned and looked toward the family room. Then moved to the doorway and peeked in.

(he's in the living room and peeks into the family room)

- Is 'in' correct? Is 'inside' a better choice?

- Is 'peeked' a good choice if he's afraid someone is in the family room and he doesn't want to be seen before entering?

Comments  
anonymousIs 'in' correct?

Yes.

anonymousIs 'inside' a better choice?

No. It isn't wrong, but it isn't as good because it's unnecessary.

anonymousIs 'peeked' a good choice if he's afraid someone is in the family room and he doesn't want to be seen before entering?

Yes.