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

If $a = b$ and $c\neq 0,$ then $a \div c = b \div c.$

The Division Property of Equality also holds true if $a,$ $b,$ and $c$ are complex numbers as long as $c\neq 0.$ This property is one of the Properties of Equality that can be used when solving equations. $\begin{aligned} 5x&=10\\ 5x\textcolor{blue}{\,\div{\,5}}&=10\textcolor{blue}{\,\div{\,5}}\\ x&=2 \end{aligned}$ 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.