ALGEBRA

# Algebraic equalities

An **equation** is an algebraic equality that is true only for some values of the variables. These values are called **solutions** of the equation.

An **identity** is an algebraic equality that is true for all values of the variables.

Example:

a + a = 2a is an identity

x + 7 = 9 is an equation. x = 2 is the solution

x + y = 5 is an equation. x = 8 and y = -3 is a solution

**Exercise**: decide if the following equalities are identities or equations:

a) x + 3x = 4x

b) 2a + 7 = 9a

c) (a + b)^{2} = a^{2} + b^{2} + 2ab

d) a + 3b = 7

Solutions: a) Identity; b) Equation; c) Identity; d) Equation

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