Pronunciation: /ɪˈkweɪ ʒən/ ?

An equation is a mathematical statement that two things are equal to each other or that two things are conditionally equal to each other.[1] If an equation is true for all values of any variables in the equation, it is called an identity. Identities are sometimes written using the symbol to indicate that it is always true.

a + 0 ≡ aThe additive identity
a · 1 ≡ aThe multiplicative identity.
sin(θ)2 + cos(θ)2 ≡ 1The Pythagorean Identity is one of the trigonometric identities.
Table 1: Examples of identities

If an equation is not true for all values of the variables, it is called a conditional equation. The values of the variables for which the equation is true is called the solution of the equation.

x = 5This is a simple equation.This is equation is true only when x = 5.
y = x + 1This is a linear equation.This equation is true for a set of ordered values (x,y) such that y = x + 1.
a2 + 2a + 4 = 0This is a quadratic equation.This equation is true only when a = -2

Solving an Equation

An equation can be solved using the various property of real numbers and the properties of equality. When solving a one variable equation, the goal is to get the variable by itself on one side of the equation.

Example 1: Solve x+5=2
x+5=2This is the equation to solve.
(x+5)-5=2-5Apply the Subtraction property of equality.
(x+5)+(-5))=2-5Apply the Definition of subtraction.
x+(5+(-5))=2-5Apply the Distributive property of multiplication over addition and subtraction.
x+0=-3Simplify both sides of the equation.
x=-3Apply the Property of addition by zero.
Table 1: Solving an equation.


  1. equation. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=equation&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 18. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n35/mode/1up/search/equation.
  3. Jones, Burton. Elementary Concepts of Mathematics, pp 141-144. MacMillan and Company, 1947. (Accessed: 2010-01-12). http://www.archive.org/stream/elementaryconcep029487mbp#page/n162/mode/1up/search/equations.
  4. Theresa R. Fitzgerald. Math Dictionary for Kids: The Essential Guide to Math Terms, Strategies, and Tables, pg 34. Prufrock Press, 1 October 2005.

Educator Resources

  • Optics and Algebra. NASA Connect. NASA LaRC Office of Education. 2010-02-18. http://www.archive.org/details/NasaConnect-Mmou-OpticsAndAlgebra.

Printed Resources

Cite this article as:

Equation. 2010-01-25. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/equation.html.


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Revision History

2010-01-25: Rewrote article, added "References" (McAdams, David.)
2008-07-16: Added 'Solving an Equation' (McAdams, David.)
2008-02-05: Change javascript vocabulary to link (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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