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Example: Form an Equation

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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

(Our solved example in mathguru.com uses this concept)


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.




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. (Our solved example in mathguru.com uses this concept)

To be precise, what is sought are often not necessarily actual values, but, more in general, mathematical expressions. 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).



