Home › Math Foundations › Algebra & Equations

Algebra & Equations

Overview

Build the foundation for all higher mathematics by understanding how equations, formulas, ratios, and scaling work together.

Core Concepts Covered

✔ Variables and expressions
✔ Solving one-step and multi-step equations
✔ Isolating variables in formulas
✔ Ratios, proportions, and cross-multiplication
✔ Real-world scaling and dimensional reasoning

Interactive Application

Each concept includes clear explanations, step-by-step examples, and guided practice with linked calculators for hands-on reinforcement.

Select a concept or jump directly into a calculator below to begin.

Lessons

Understanding Order of Operations

Master PEMDAS with pure arithmetic — learn why the order of operations exists, how to apply it step by step, and the most common mistakes that trip people up.

Variables and Expressions

Learn what variables and algebraic expressions are, how to write them from word descriptions, and how to evaluate them by substituting values.

Order of Operations (PEMDAS) with Variables

Apply PEMDAS correctly to algebraic expressions — avoiding the most common mistakes students make when simplifying and evaluating.

Combining Like Terms

Simplify algebraic expressions by identifying and combining like terms — the essential skill for solving any equation.

Solving One-Step Equations

Use inverse operations to isolate a variable in one move — the foundation of all equation solving.

Solving Two-Step Equations

Solve equations that require two inverse operations — and translate real-world scenarios into two-step equations you can solve.

Solving Multi-Step Equations

Solve equations with variables on both sides, parentheses, and multiple steps — including translating complex word problems into equations.

Introduction to Inequalities

Understand inequality symbols, solve one- and two-step inequalities, graph solutions on a number line, and learn why multiplying by a negative flips the symbol.

Graphing on the Coordinate Plane

Plot points and linear equations on the coordinate plane, identify x- and y-intercepts, and build a table of values to sketch any line.

Slope and Linear Relationships

Calculate and interpret slope as a rate of change, use slope-intercept and point-slope forms, and identify parallel and perpendicular lines.

Evaluating Functions

Understand function notation f(x), evaluate functions at given inputs, interpret domain and range, and see how functions model real-world relationships.

📝

Take the Algebra & Equations Quiz

Test your knowledge across all lessons — 25 or 50 questions, randomly drawn

Calculators

Algebra I 3 Foundations Active

One-Step Equation Solver

Solve basic linear equations with one operation (addition, subtraction, multiplication, or division).

Tutorial Ready

PEMDAS / Order of Operations Calculator

Evaluate numerical expressions following the correct order of operations: Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction.

Tutorial Ready

Two-Step Equation Solver

Solve linear equations that require two steps: reversing addition/subtraction and then reversing multiplication/division.

Tutorial Ready

Pre-Calculus 3 Foundations Active

Complex Number Calculator

Perform addition, subtraction, multiplication, and division on complex numbers (a + bi).

Tutorial Ready

Function Evaluation

Evaluate any function f(x) by substituting a value and computing the result step by step.

Tutorial Ready

Parabola Vertex Calculator

Find the vertex (h, k) of a parabola given in standard form.

Tutorial Ready