Theory

# Division Property of Equality

When rewriting equations it's important to make the the same operation on both sides to ensure that the equality still holds. So, if one side is divided by a number, the other side must be divided by the same number. In the equation $3x=12$ both sides is divided by $3$ to solve for $x.$ $\dfrac{3x}{{\color{#FF0000}{3}}}=\dfrac{12}{{\color{#FF0000}{3}}} \quad \Leftrightarrow \quad x=4$ Remember that division by zero is undefined, so, for example, by dividing both sides by $x$ it is assumed that $x$ cannot be zero.