Inverse operations are two operations that, all else being equal, undo one another. For instance, adding $6$ and subtracting $6$ are inverse operations because they cancel each other out. $\begin{aligned} &x + 6 {\color{#0000FF}{\ -\ 6}} \\ &x \,\cancel{\,+ \,6}\, \cancel{{\color{#0000FF}{\ -\ 6}}} \\ &x \end{aligned}$ When using inverse operations on an equation, in order to follow the Properties of Equality, any operation performed on one side of an equation must also be performed on the other side to maintain equality. $\begin{aligned} x\div{2} &=1 \\ x\div{2}{\color{#0000FF}{\ \times{\ 2}}}&=1{\color{#0000FF}{\ \times{\ 2}}}\\ x&=2 \end{aligned}$ In this case, the division by $2$ on one side of the equation could only be eliminated by a multiplication by $2$ on both sides of the equation. The result of applying the Properties of Equality on an equation is an equivalent equation.