Algebra Foundations

Introduction to Variables

What a variable represents and how to use one in an expression.

Foundational10 min lesson1 min readUpdated August 12, 2026Author not yet attributed

What Is a Variable?

In algebra, a variable is a letter that stands in for a number we don't know yet, or a number that can change. Instead of writing a blank or a question mark, mathematicians write a letter like x, y, or n.

Definition — Variable

A symbol, usually a letter, that represents an unknown or changeable numeric value.

x + 5 = 12

(1)

Example — Finding x

In the equation above, x stands for the number that makes the equation true. Since 7 + 5 = 12, x = 7.

Equation Editor

Edit as raw LaTeX

sum(i, 1, n, i^2) = n(n+1)(2n+1)/6

Constants

Structures

Calculus & discrete math

Greek

\sum_{i=1}^{n} i^{2} = \frac{\operatorname{n}\left(n + 1\right) \cdot \left(2 \cdot n + 1\right)}{6}

Evaluate

Unknown function "n"

Practice Tip

Tip

Try substituting your answer back into the original equation — if both sides match, you found the right value.

Common Mistakes

Treating a variable as if it always equals the same number in every problem.
A variable's value depends on the specific equation or expression it appears in.

Key Takeaways

A variable represents an unknown or changeable value.
You can solve for a variable's value using inverse operations.

Vocabulary

Variable: A letter representing an unknown or changeable value.
Constant: A fixed value that does not change, like the 5 in x + 5 = 12.

Summary

Variables let us write general, reusable equations and expressions instead of one for every possible number.

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