Editing Elementary algebra (section)

{{short description|Basic concepts of algebra}}
{{Image frame|align=right|width=200|caption=The [[quadratic formula]], which is the solution to the [[quadratic equation]] <math>ax^2+bx+c=0</math> where <math>a\neq0</math>. Here the symbols {{mvar|a}}, {{mvar|b}}, and {{mvar|c}} represent arbitrary numbers, and {{mvar|x}} is a variable which represents the solution of the equation.|content=<math>\overset{}{\underset{}{ x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} } }</math>}}
[[File:Polynomialdeg2.svg|thumb|right|200px|Two-dimensional plot (red curve) of the algebraic equation <math>y = x^2 - x - 2</math>.]]

'''Elementary algebra''', also known as '''high school algebra''' or '''college algebra''',<ref>Pierce, R., [https://www.mathsisfun.com/algebra/index-college.html College Algebra], ''Maths is Fun'', accessed 28 August 2023</ref> encompasses the basic concepts of [[algebra]]. It is often contrasted with [[arithmetic]]: arithmetic deals with specified [[number]]s,<ref>[[Herbert Ellsworth Slaught|H.E. Slaught]] and N.J. Lennes, ''Elementary algebra'', Publ. Allyn and Bacon, 1915, [https://books.google.com/books?id=gLii_eO4dNsC&dq=%22Elementary%20algebra%22%20letters&pg=PA1 page 1] (republished by Forgotten Books)</ref> whilst algebra introduces [[variable (mathematics)|variables]] (quantities without fixed values).<ref>Lewis Hirsch, Arthur Goodman, ''Understanding Elementary Algebra With Geometry: A Course for College Students'', Publisher: Cengage Learning, 2005, {{ISBN|0534999727}}, 9780534999728, 654 pages, [https://books.google.com/books?id=7hdK4RSub5cC&q=generalization&pg=PA2 page 2]</ref>

This use of variables entails use of algebraic notation and an understanding of the general rules of the [[Operation (mathematics)|operations]] introduced in arithmetic: addition, subtraction, multiplication, division, etc. Unlike [[abstract algebra]], elementary algebra is not concerned with [[algebraic structure]]s outside the realm of [[real number|real]] and [[complex number]]s.

It is typically taught to [[secondary school]] students and at introductory college level in the [[United States]],<ref name=leff /> and builds on their understanding of [[arithmetic]]. The use of variables to denote quantities allows general relationships between quantities to be formally and concisely expressed, and thus enables solving a broader scope of problems. Many quantitative relationships in [[science]] and mathematics are expressed as algebraic [[equation]]s.