Algebra

Identity

A statement that is true for every value of the variable. Uses the ≡ symbol.

Definition

An identity, unlike an equation, is true for all values of the variable. (x + 1)² ≡ x² + 2x + 1 is an identity because it holds for every x.

Example

2(x + 3) ≡ 2x + 6 is an identity.

Common confusion

An equation x + 5 = 12 is true only for x = 7. An identity is true everywhere.

Related terms

Equation

A mathematical statement with an equals sign — true for some specific value(s) of the unknown.

Expression

A combination of numbers, letters and operations with no equals sign, e.g. 3x + 5.

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