Algebra
Functions in Algebra: f(x), Zeros, Domain and Range
Learn what a function is, how to read and evaluate f(x), make a function table, find the zeros and work out the domain and range, with…
Algebra Guides for Beginners
Free algebra guides for beginners: variables, expressions, equations, formulas and polynomials, explained step by step with examples you can check on the calculator.
Algebra
Algebraic Expressions: How to Evaluate and Simplify
Learn how to evaluate an algebraic expression by substitution and simplify it by combining like terms, with clear worked examples and practice problems.
Algebra
How to Solve for x: Step-by-Step Guide With Examples
Learn how to solve for x step by step: one-step, two-step and multi-step equations, fractions, decimals and solving for y, with worked examples and practice.
Algebra
Algebra Basics: A Beginner’s Guide to Variables, Expressions and Equations
Learn algebra basics in plain words: variables, terms, expressions and equations, how to simplify, how to solve for x step by step and how to check…
What Is Algebra?
Algebra is the part of math that uses letters, called variables, to stand for numbers you do not know yet. It turns word problems into short equations, such as x + 7 = 12, and gives you a few simple rules to find the missing value. Every topic below, from expressions to polynomials, builds on that one idea.
In short: Algebra is arithmetic with an unknown number written as a letter, solved by keeping both sides of an equation in balance.
Your Algebra Learning Path
New to algebra? Work through these steps in order. Each one links to the guide that covers it, starting with our algebra basics guide.
- Learn the key words: variable, coefficient, constant, term and like terms.
- Tell an expression from an equation, so you know whether to simplify or solve.
- Evaluate and simplify expressions by substitution, combining like terms and the distributive property.
- Solve for x in one-step, two-step and multi-step equations, including fractions.
- Check every answer by substituting it back into the equation.
- Move on to functions: f(x) notation, zeros, domain and range.
Basic Algebra Formulas
| Formula | Rule | Example |
|---|---|---|
| Distributive property | a(b + c) = ab + ac | 3(x + 4) = 3x + 12 |
| Square of a sum | (a + b)² = a² + 2ab + b² | (x + 3)² = x² + 6x + 9 |
| Square of a difference | (a − b)² = a² − 2ab + b² | (x − 2)² = x² − 4x + 4 |
| Difference of squares | a² − b² = (a + b)(a − b) | x² − 25 = (x + 5)(x − 5) |
| Slope of a line | m = (y₂ − y₁) ÷ (x₂ − x₁) | (1, 2) to (3, 8): m = 6 ÷ 2 = 3 |
| Quadratic formula | x = (−b ± √(b² − 4ac)) ÷ 2a | x² − 5x + 6 = 0 gives x = 2 or 3 |
More formulas for trigonometry, geometry and statistics are on our math formulas cheat sheet.
How to Check an Algebra Answer
Substitute your answer for the letter and work out both sides. If they match, the answer is right. For 3x + 5 = 20 with x = 5, type 3×5+5 into the CalcSolver calculator and you get 20, so the answer works. To solve the whole equation step by step, use our free solve for x calculator. It is the fastest way to catch a sign error before you hand in your homework.
In short: Solve the steps yourself, then substitute the answer on a calculator. Matching sides mean a correct answer.
Algebra: Frequently Asked Questions
What topics does basic algebra cover?
Basic algebra covers variables and expressions, combining like terms, the distributive property, solving linear equations, inequalities, working with formulas and an introduction to polynomials and factoring.
What is the best way to learn algebra?
Learn the key words first, then practise a few problems of one type at a time. Say each step out loud, keep both sides of the equation balanced, and check every answer by substitution.
Is there a free algebra solver?
CalcSolver is a free calculator for checking algebra answers: substitute your value and confirm both sides are equal. Our step-by-step guides show the method, so you understand each step instead of only copying a result.