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Elementary algebra is a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic. While in arithmetic only numbers and their arithmetical operations (such as +, −, ×, ÷) occur, in algebra one also uses symbols (such as x and y, or a and b) to denote numbers. These are called variables. This is useful because:
- It allows the generalization of arithmetical equations (and inequalities) to be stated as laws (such as a + b = b + a for all a and b), and thus is the first step to the systematic study of the properties of the real number system.
- It allows reference to numbers which are not known. In the context
of a problem, a variable may represent a certain value of which is
uncertain, but may be solved through the formulation and manipulation
of equations.
- It allows the exploration of mathematical relationships between quantities (such as "if you sell x tickets, then your profit will be 3x − 10 dollars").
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