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).

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

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