---
title: Inequalities
description: Inequalities are mathematical statements comparing the relative size of two values or expressions using inequality symbols. Learners will understand how to solve, graph, and interpret linear, quadratic, and absolute value inequalities in one or more variables.
category: mathematics
subcategory: algebra
difficulty: beginner, intermediate, advanced
url: /subject/inequalities
---

# Inequalities

Inequalities are mathematical statements comparing the relative size of two values or expressions using inequality symbols. Learners will understand how to solve, graph, and interpret linear, quadratic, and absolute value inequalities in one or more variables.

## Available Resources

4 Courses • 3 Websites

## Websites

### 1. Art of Problem Solving Wiki: Inequalities

Competition-math wiki page from Art of Problem Solving surveying the standard inequalities: AM-GM, Cauchy-Schwarz, Jensen, rearrangement, Hölder and others, with statements, proofs and links to olympiad problems. Prepares students to recognize and apply these tools in contest proofs.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://artofproblemsolving.com/wiki/index.php/Inequalities

**Tags:** inequalities, am-gm-inequality, cauchy-schwarz-inequality, olympiad-math, competition-math

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

### 3. mathsisfun.com

MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathsisfun.com

**Tags:** websites, mathematics-statistics, algebra

## Courses

### 1. Algebra: Inequalities

Master inequalities! This Algebra course from Sal Khan et al. explains solving, graphing, and applying inequalities.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq

**Tags:** inequalities, linear-inequalities, algebra, graphing-inequalities, compound-inequalities

### 2. Inequalities

Master inequalities! This course covers techniques & problem-solving, perfect for math competitions and beyond. Join AoPS!

**Difficulty:** Advanced | **Price:** Paid

**Link:** https://artofproblemsolving.com/school/course/ineq20

**Tags:** inequalities, olympiad-math, am-gm-inequality, cauchy-schwarz, competition-math

### 3. College Algebra

Coursera course: Basic Math: Algebra

**Difficulty:** Beginner | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/basic-math-algebra

**Tags:** courses, mathematics-statistics, algebra

### 4. Algebra: Elementary to Advanced - Polynomials and Roots

**Author:** Joseph W. Cutrone

Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework.

**Difficulty:** Beginner | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/polynomials-roots

**Tags:** polynomials, factoring, exponents, radicals, algebra

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