# Equivalent transformation

In **equivalence transformation**, an equation is reformed without changing the solution set of the equation. Often one uses the equivalence transformation to solve an equation. In doing so, the sought variable is isolated (the equation is solved for the variable).

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### Remember

**Addition and subtraction rule**

If both sides of the equation are added or subtracted by the same number, the solution set of the equation does not change.

**Multiplication and division rule**

If both sides of the equation are multiplied or divided by the same number other than 0, the solution set of the equation does not change.

### Examples

#### Addition and subtraction

$x+10=18 \quad|\color{red}{-10}$$x+10\color{red}{-10}=18\color{red}{-10}$

$x=8$

#### Multiplication and division

$5x=25 \quad|\color{red}{:5}$$\frac{5x}{\color{red}{5}}=\frac{25}{\color{red}{5}}$

$x=5$