Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often denoted by symbols (such as a, n, x, y or z). This is useful because:
- 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 + 1 = 10" or going a bit further "Find a number x such that ax + b = c". This step leads to the conclusion that it is not the nature of the specific numbers that allows us to solve it, but that of the operations involved.)
- It allows the formulation of functional relationships. (For instance, "If you sell x tickets, then your profit will be 3x − 10 dollars, or f(x) = 3x − 10, where f is the function, and x is the number to which the function is applied.")
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Other articles related to "elementary algebra, algebra":
... Equations involving linear or simple rational functions of a single real-valued unknown, say x, such as can be solved using the methods of elementary algebra. ...
... Algebra is a branch of mathematics concerning the study of structure, relation, and quantity ... Elementary algebra is the branch that deals with solving for the operands of arithmetic equations ... Modern or abstract algebra has its origins as an abstraction of elementary algebra ...
... When the multiplicity is only partial (meaning that for example, only the left hand sides of the equations are multiples, while the right hand sides are not or not by the same number) then the system is unsolvable ... For example, in the second equation yields that which is in contradiction with the first equation ...
... comes from Boole's interpretation of logic as an elementary algebra ... is also used, in spite of the ambiguity coming from the fact that the + of ordinary elementary algebra is an exclusive or when interpreted logically in a two-eleme ... from Boole's interpretation of logic as an elementary algebra over the two-element Boolean algebra other notations include to be found in Peano ...
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