# Equation

Pronunciation: /ɪˈkweɪ.ʒən/ Explain

An equation is a mathematical statement that two things are equal to each other or that two things are conditionally equal to each other. 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 they are always true.

IdentityDescription
a + 0 ≡ a The additive identity
a · 1 ≡ a The multiplicative identity
sin(θ)2 + cos(θ)2 ≡ 1 The 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.

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

### How to Solve 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
EquationDiscussion
x + 5 = 2This is the equation to solve.
(x + 5)- 5 = 2 - 5 Apply the Subtraction property of equality
(x + 5) + (-5)) = 2 - 5 Apply the Definition of subtraction
x + (5 + (-5)) = 2 - 5 Apply the Distributive property of multiplication over addition and subtraction.
x + 0 = -3 Simplify both sides of the equation.
x = -3 Apply the property of addition by zero
Table 1: Solving an equation.
1. McAdams, David E.. All Math Words Dictionary, equation. 2nd Classroom edition 20150108-4799968. pg 71. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 18. www.archive.org. International Textbook Company. January 1963. Last Accessed 7/9/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n35/mode/1up/search/equation. Buy the book
3. Jones, Burton. Elementary Concepts of Mathematics. pp 141-144. www.archive.org. MacMillan and Company. 1947. Last Accessed 7/9/2018. http://www.archive.org/stream/elementaryconcep029487mbp#page/n162/mode/1up/search/equations. Buy the book
4. Theresa R. Fitzgerald. Math Dictionary for Kids: The Essential Guide to Math Terms, Strategies, and Tables. pg 34. Prufrock Press. 1 October 2005. Last Accessed 7/9/2018. Buy the book

### Educator Resources

• Optics and Algebra. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Mmou-OpticsAndAlgebra/index.htm.

McAdams, David E. Equation. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/e/equation.html.

### Revision History

4/20/2019: Updated expressions and equations to match new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)