Take it off both sides

A chalk box holds some sticks. Seven more lie on the tray. Together there are twelve. Let x be the sticks in the box.

Lift the same amount from both pans

Start with x + 7 = 12. Picture x + 7 sticks in the left pan and 12 in the right. Lift seven sticks from each pan. Both pans lose the same amount, so the beam stays level.

On the left, x + 7 loses 7 and leaves x. On the right, 12 − 7 = 5. So x = 5.

Rule: Add or take away the same number on both sides. The solution stays the same.

The move also undoes a subtraction. In x − 4 = 6, add 4 to both sides. On the left, x − 4 + 4 is x. On the right, 6 + 4 = 10. So x = 10.