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Basic Algebra — A Beginner's Guide

Algebra is one of the most important branches of math, and it shows up everywhere — from science class to everyday problem-solving. This guide breaks down the basics so you can start solving equations with confidence.

What Is Algebra?

Algebra is the branch of mathematics that uses letters and symbols to represent unknown numbers. Instead of working only with specific values like 5 or 12, algebra lets you write general rules and solve for values you don't know yet. If you've ever seen an equation like x + 3 = 10, you've already encountered algebra.

Variables and Expressions

In algebra, letters like x and y are called variables — they stand in for numbers we don't know yet. When you combine variables with numbers and operations, you get an expression.

Example: In the expression 3x + 5:

  • 3x and 5 are the terms
  • 3 is the coefficient (the number multiplied by the variable)
  • x is the variable
  • 5 is a constant (a fixed number with no variable)

An expression is different from an equation. An expression has no equals sign — it's just a combination of terms. An equation sets two expressions equal to each other so you can solve for the unknown.

Solving One-Step Equations

A one-step equation can be solved in a single operation. The goal is to get the variable by itself on one side of the equals sign by doing the inverse operation.

Example 1 — Addition:

x + 7 = 12

Subtract 7 from both sides: x = 12 - 7

x = 5

Example 2 — Multiplication:

3x = 18

Divide both sides by 3: x = 18 / 3

x = 6

Solving Two-Step Equations

Two-step equations require two operations to isolate the variable. The general strategy is to undo addition or subtraction first, then undo multiplication or division.

Example:

2x + 3 = 11

Step 1 — Subtract 3 from both sides: 2x = 8

Step 2 — Divide both sides by 2: x = 4

x = 4

Common Algebra Formulas

Here are some of the most commonly used algebra formulas you'll encounter in school:

Slope-Intercept Form

y = mx + b where m is the slope and b is the y-intercept.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a — used to solve any quadratic equation in the form ax² + bx + c = 0.

Distance Formula

d = √((x₂ - x₁)² + (y₂ - y₁)²) — finds the distance between two points on a coordinate plane.

See all formulas on our Formula Sheet →

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