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Variable

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A variable is a symbol used to represent either a quantity which is unknown (for example, the solutions of a quadratic equation) or a quantity which may change (that is, which may vary).

Variables are very useful in solving many problems algebraicly. For instance, word problems can often be solved using variables to represent desired but unknown expressions.

Any symbol may be used as a variable, but the most common variables are x, y, z, m, n, a, b, c, p, q, and many Greek letters.

By convention, certain variables are often used for certain types of quantities. z, w, \omega and \zeta are often used as complex variables. m and n are often used as variables representing integers. p and q are often used as variables representing prime numbers. And a, b and c are often used as variables representing geometric quantities such as length.


Contents

Problems

Preintroductory

  • What number, when added to 7, gives a sum of 10? (Source)

Introductory

Intermediate

Olympiad

Want to learn how to tackle those tough AMC/AIME/Olympiad algebra problems? Check out Art of Problem Solving's Intermediate Algebra by Richard Rusczyk and Mathew Crawford. Over 1600 problems!
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