An *identity* is an equation that is true regardless of what values are substituted in for its variables.

Examples:

A *conditional equation* is an equation that is true only for certain values of its variables.

Examples:

Isolating a variable means rearranging and modifying an equation, according to the rules of algebra, so that a variable is all by itself on one side of the equation. If we started off with the equation

, we could add to both sides of the equation to end up with . The variable is now isolated.