An equation tells us that two expressions have equal value. For example, if and have equal value, we can write the equation

Earlier, we used hangers to understand that if we add the same positive number to each side of the equation, the sides will still have equal value. It also works if we add negative numbers! For example, we can add -9 to each side of the equation.

Because expressions represent numbers, we can also add expressions to each side of an equation. For example, we can add to each side and still maintain equality.

If we multiply or divide the expressions on each side of an equation by the same number, we will also maintain the equality (as long as we do not divide by zero).

or

Now we can see that is the solution to our equation.