**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 3*x*+ 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 3*x*− 10 dollars, or*f*(*x*) = 3*x*− 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":

Equation Solving - Methods of Solution -

... single real-valued unknown, say x, such as can be solved using the methods of

**Elementary Algebra**... single real-valued unknown, say x, such as can be solved using the methods of

**elementary algebra**...**Elementary Algebra**- Solving Algebraic Equations - Relation Between Solvability and Multiplicity

... 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 ...

History Of

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**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**...Common Logical Connectives - History of Notations

... comes from Boole's interpretation of logic as an

... comes from Boole's interpretation of logic as an

**elementary algebra**... symbol + 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-element ring punctually in. 1 comes from Boole's interpretation of logic as an**elementary algebra**over the two-element Boolean**algebra**other notations include to be found in Peano ...### Famous quotes containing the words algebra and/or elementary:

“Poetry has become the higher *algebra* of metaphors.”

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“Listen. We converse as we live—by repeating, by combining and recombining a few elements over and over again just as nature does when of *elementary* particles it builds a world.”

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