Elementary algebra

:This article is about basic algebra in mathematics. For other uses of the term "algebra" see algebra (disambiguation).

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Elementary algebra is the most basic form of algebra taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. While in arithmetic only numbers and their arithmetical operations (such as +, −, ×, ÷) occur, in algebra one also uses symbols (such as a, x, y) to denote numbers. This is useful because:

Related Topics:
Algebra - Mathematics - Arithmetic - Number

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• It allows the general formulation of arithmetical laws (such as $a\; +\; b\; =\; b\; +\; a$ for all a and b), and thus is the first step to a systematic exploration of the properties of the real number system.
• It allows the reference to "unknown" numbers, the formulation of equations and the study of how to solve these (for instance "find a number x such that $3x\; +\; 2\; =\; 10$).
• It allows the formulation of functional relationships (such as "if you sell x tickets, then your profit will be $3x\; -\; 10$ dollars").

These three are the main strands of elementary algebra, which should be distinguished from abstract algebra, a much more advanced topic generally taught to college seniors.

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In algebra, an "expression" may contain numbers, variables and arithmetical operations; a few examples are:

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:x + 3,

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:y^{2} - 3,

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:z^{7} + a(b + x^{3}) + 42/y - pi.,

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An "equation" is the claim that two expressions are equal. Some equations are true for all values of the involved variables (such as a + (b + c) = (a + b) + c); these are also known as "identities". Other equations contain symbols for unknown values and we are then interested in finding those values for which the equation becomes true: x^{2} - 1 = 4. These are the "solutions" of the equation.

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