Equation

An equation is a mathematical statement that asserts the equality of two expressions. Equations consist of the expressions that have to be equal on opposite sides of an equal sign as in

Properties

If an equation in algebra is known to be true, the following operations may be used to produce another true equation:

1. Any real number can be added to both sides.

2. Any real number can be subtracted from both sides.

3. Any real number can be multiplied to both sides.

4. Any non-zero real number can divide both sides.

5. Some functions can be applied to both sides. Caution must be exercised to ensure that the operation does not cause missing or extraneous solutions. For example, the equation y*x=x has 2 solutions: y=1 and x=0. Dividing both sides by x "simplifies" the equation to y=1, but the second solution is lost.

http://en.wikipedia.org/wiki/Equation

Equation solving

In mathematics, to solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality). These expressions contain one or more unknowns, which are free variables for which values are, sought that cause the condition to be fulfilled.

A solution of the equation is an assignment of expressions to the unknowns that satisfies the equation; in other words, expressions such that, when they are substituted for the unknowns, the equation becomes a tautology (a provably true statement). (Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Equation_solving

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