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Inverse Operations

Concept

Inverse Operations

Inverse operations are two operations that, all else being equal, undo one another. For instance, adding 66 and subtracting 66 are inverse operations because they cancel each other out. x+6x+6  6x\begin{aligned} &x+6\\ &x+6{\color{#0000FF}{\ -\ 6}}\\ &x \end{aligned} In an expression like x+6,x+6, the addition of 66 to xx is eliminated by performing the inverse operation: a subtraction of 6.6. 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. x÷2=1x÷2 × 2=1 × 2x=2\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 22 on one side of the equation could only be eliminated by a multiplication by 22 on both sides of the equation. The result of applying the Properties of Equality on an equation is an equivalent equation.