A library bought 45 more books and later lent out 78 of them; 267 books now remain on its shelves. How many were there to begin with?

When you're comfortable with the balance method, you can move terms across the '=' sign in one step by **flipping the sign** of the term that moves.

$3x+2=11$
→ move +2 across, flipping it to −2: $3x=11-2=9$
→ $x=9÷3=3$

For the multiplier: move ×3 across as ÷3 (and ÷ moves across as ×). Same balance idea, faster notation. **The sign flips because addition and subtraction are inverses, multiplication and division are inverses.**