Given an equation, dividing each side of the equation by the same non-zero number yields an equivalent equation.

The Division Property of Equality also holds true if $a,$ $b,$ and $c$ are complex numbers as long as $c\ne 0.$ This property is one of the Properties of Equality that can be used when solving equations. $$\begin{array}{rl}5x& =10\\ 5x÷5& =10÷5\\ x& =2\end{array}$$ To isolate the variable, the multiplication by $5$ can be eliminated by dividing both sides of the equation by $5,$ since division is the inverse operation of multiplication.