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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.