Variable

Variable

A quantity that can change or that may take on different values. Variable also refers to a letter or symbol representing such a quantity.

See also

Multivariable

Worked Example

Problem: In the expression

3x + 5

, identify the variable and evaluate the expression when the variable equals 4.

Step 1: Identify the variable. The letter

x

is the variable because it represents a quantity that can take on different values.

Step 2: Substitute the given value into the expression by replacing

x

with 4.

3(4) + 5

Step 3: Simplify the expression.

12 + 5 = 17

Answer: The variable is

x

, and when

x = 4

, the expression equals 17.

Variables allow you to write general rules and relationships instead of working with only specific numbers. For instance, the area formula

A = lw

uses variables to describe how area works for every rectangle, not just one. Without variables, algebra, equations, and functions would not exist.

Mistake: Thinking a variable always represents one specific unknown number.

Correction: A variable can represent a single unknown (as in the equation

x + 3 = 10

), but it can also represent a quantity that takes on many values, such as

x

in the function

f(x) = 2x

. Context determines whether a variable stands for one value or many.