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.^[2] 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.

Identity	Description
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.

Equation	Description	Solution
x = 5	This 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

Equation	Discussion
x + 5 = 2	This 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.

References

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.

Cite this article as:

McAdams, David E. Equation. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://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.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/25/2010: Rewrote article, added "References". (McAdams, David E.)
7/16/2008: Added 'Solving an Equation'. (McAdams, David E.)
2/5/2008: Change javascript vocabulary to link. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)