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*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.
$\begin{aligned}
&x+6\\
&x+6{\color{#0000FF}{\ -\ 6}}\\
&x
\end{aligned}$
In an expression like $x+6,$ the addition of $6$ to $x$ is eliminated by performing the inverse operation: a subtraction of $6.$ Using inverse operations on an equation, however, is a little different: in order to adhere to 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.