Using inverse operations to solve equations

Inverse operations undo each other

Inverse operations are operations that are opposite or “undo” each other.

For example, addition undoes subtraction and division undoes multiplication.

Inverse operations are useful when solving equations.

Inverse operation examples:

Addition/Subtraction $x+3-3=x$

Multiplication/Division $x\cdot3\div3=x$

Exponents/Roots $\sqrt{x^2}=x$

Example

Use inverse operations to complete the equation.

$2+7\quad?\quad=7$

In this example $2$ is being added to $7$ , to undo that operation we need to subtract by $2$ .

$2+7-2=7$

Simplify to show that the equation is true.

$2-2+7=7$

$0+7=7$

$7=7$

Let’s try another example of inverse operations.

Example

Use inverse operations to complete the equation.

$4\cdot3\quad?\quad=4$

In this example $4$ is being multiplied by $3$ , to undo that operation we need to divide by $3$ .

$4\cdot3\div3=4$

Simplify to show that the equation is true.

$4\cdot1=4$

$4=4$