Variable

A variable is often denoted by a letter in an algebraic expression and represents a value which can be changed or varied. For example, in the expression x + 2, the letter x is a real variable and can take on the value of any real number. If x is 4 then the expression has a value of 6 because 4 + 2 = 6. Similarly, if x is 10 the expression has a value of 12. The number 2 in this expression is known as a constant because it never changes. Generally, a constant can be any number or letter in an equation whose value does not change.

In an equation, the value of a variable is often not given and is therefore called an unknown. In the equation y + 7 = 12, the letter y is an unknown variable and it represents some number. The value of the unknown which makes the equation true is called the solution or root of the equation. In this example, the solution of the equation is y = 5 because 5 + 7 = 12. Often, there is more than one solution to an equation so the unknown variable is equal to all of these values. The solution to the equation x² = 4 is both 2 and -2 because each of these values make the equation true.