Rule

Properties of Equality

For their respective operations, the Addition, Subtraction, Multiplication, and Division Properties of Equality state that performing the same operation on each side of an equation yields an equivalent equation.

Property of Equality	Algebraic Representation
Addition	If $a = b,$ then $a + c = b + c$
Subtraction	If $a = b,$ then $a - c = b - c$
Multiplication	If $a = b,$ then $a \cdot c = b \cdot c$
Division	If $a = b$ and $c \neq 0,$ then $\dfrac{a}{c} = \dfrac{b}{c}$

These properties can be used together with inverse operations to isolate the variable in an equation.

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