A bookshelf can hold a maximum of 45 books. Let b represents the number of books to be shelved. Which inequality represents how many books can be put on the shelves?
The number of books that can be shelved is 45. So then we know that the amount that need to be shelved can be 45, if the bookshelf had 0 books on it. This means that it can have the equal part of the inequality sign.
However, the amount of book that need to be shelved cannot exceed 45, so b must be less than 45.