Algebraic language

# 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 equations or identities:

a) x + y + z = 28

b) x·(x+5) = x^{2} +5x

c) x^{2} - 5x + 4 = x^{2} +25x

d) (x+1)^{2} = x^{2} + 2x +1

Solutions: a) equation; b) identity; c) equation; d) identity

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