Equation

This article is about equations in mathematics. For equations in chemistry, see Chemical equation.

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In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. Equations are examples of open sentences. In equations, the values of the variables for which the equation is true are called solutions.

For example

(x + 1)² = x² + 2x + 1

is an identity, while

x² - 5x + 6 = 0

is an equation, whose solutions are 2 and 3.

Letters from the beginning of the alphabet like a, b, c, ... are often considered constants in the context of the discussion at hand, while letters from end of the alphabet, like x, y, z, are usually considered variables. Thus to solve the equation, one must express those values of the variables that are solutions in terms of whatever constants may be included.

See also Linear equation, Quadratic equation, Inequality, solution point, Trigonometric identity