Free inequality calculator with steps and graph

Solve Any Inequality Instantly

Math should feel like magic, not misery. Enter a linear, quadratic, absolute-value, rational, system, or linear two-variable inequality and get steps, notation, and a live graph in real time.

2x + 3 > 7x^2 - 5x + 6 < 0|x - 2| <= 4-3 < 2x + 1 <= 72x + 3y < 6x >= 0; y >= 0

Fast Homepage Solver

This homepage version keeps the first interaction light. Full steps, graphs, and verification stay on the dedicated calculator pages.

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Quick Result

The linear inequality isolates x to the right of 2.

linear

Interval Notation

(2, +∞)

Inequality

x > 2

Next Step

Open the detailed calculator page for the full algebra steps and graph.

Homepage Input Tips

  • Type `<`, `>`, `<=`, and `>=` directly from the keyboard.
  • Use sample buttons for the most common linear, quadratic, absolute-value, and graphing patterns.
  • Open the dedicated page when you need the number line, coordinate plane, sign chart, or full step list.

Why it feels faster

Homepage loads the quick shell first

The input box hydrates before the heavy graphing and step-by-step workspace code.

Solver stays focused on quick patterns

Common forms are handled instantly here, while detailed solving stays on the dedicated pages.

Detailed tools stay on dedicated pages

Number lines, coordinate planes, practice mode, history, and speech stay off the homepage critical path.

When to leave the homepage

Use the homepage for fast checks. Open the detailed calculator when you want full steps, graphs, interval notation, point verification, or a topic-specific workflow.

Calculator Cluster

Choose the exact inequality tool you need

Linear01

Linear Inequality Calculator

Solve one-variable linear inequalities with steps, interval notation, and a clean number-line graph.

One-Step02

One Step Inequality Calculator

Solve one-step inequalities with sign-flip detection, number line graph, and interval notation.

Two-Step03

Two Step Inequality Calculator

Solve two-step inequalities with the sign-flip rule, number line, and interval notation.

Multi-Step04

Multi Step Inequality Calculator

Solve multi-step inequalities with distribution, combining like terms, variable collection, and sign-flip detection.

Fraction05

Fraction Inequality Calculator

Solve inequalities with fraction coefficients using the LCD clearing method, with steps, number line, and interval notation.

Number Line06

Number Line Inequality Calculator

Graph any inequality on a number line with open and closed endpoint detection, shading direction, and interval notation output.

Quadratic07

Quadratic Inequality Calculator

Solve quadratic inequalities with sign analysis, roots, interval notation, and a number-line graph.

Polynomial08

Polynomial Inequality Calculator

Solve cubic, quartic, and higher-degree inequalities with sign charts, multiplicity detection, and interval notation.

Absolute Value09

Absolute Value Inequality Calculator

Solve absolute value inequalities with case splitting, interval notation, and step-by-step explanations.

Compound010

Compound Inequality Calculator

Solve compound inequalities with interval intersection, union logic, and graph output.

Rational011

Rational Inequality Calculator

Solve rational inequalities with steps, excluded values, sign charts, and interval notation.

Graphing012

Graphing Inequalities Calculator

Graph linear, quadratic, and absolute value inequalities in two variables with shading, dashed or solid boundaries, and system overlap tools.

Interval Notation013

Interval Notation Calculator

Convert inequalities to interval notation and back with steps, number-line visuals, bracket rules, and interval set operations.

Interval Converter014

Inequality to Interval Notation Calculator

Convert any inequality to interval notation with bracket rules, endpoint logic, and number line output.

Systems015

System of Inequalities Calculator

Graph 2 to 6 inequalities, highlight the feasible region, find corner points, and solve linear-programming objectives with steps.

01

How it works

Type or tap an inequality with <, >, <=, >=, powers, absolute-value bars, fractions, or x-y graphing terms.

02

How it works

Watch the calculator isolate the variable, identify critical points, or rewrite a linear boundary for coordinate-plane graphing.

03

How it works

Use the graph, notation, checker tools, and practice mode to confirm the final solution or shaded half-plane.

Learn

Build topic authority with deep inequality guides

Each guide is designed to cover a key search intent: definitions, rules, worked examples, graphing, and notation. That keeps the site useful for both search engines and actual students.

18 min read

How to Solve Inequalities

A complete guide covering the core inequality rules, when to flip the sign, and how to solve linear, multi-step, compound, fraction, absolute value, quadratic, and rational inequalities.

7 min read

How to Solve Two-Step Inequalities

A practical guide to isolating the variable in two moves — with sign-flip rules, worked examples, and number line graphs.

5 min read

Inequality Symbols

What every inequality symbol means, how strict and inclusive symbols differ, and how they connect to interval notation and number line graphs.

7 min read

Inequality Symbols: Complete Guide

A reference guide for reading inequality symbols correctly and mapping them to number-line endpoints.

8 min read

Interval Notation Explained

A compact guide to parentheses, brackets, infinity, and multi-interval answers.

6 min read

How to Graph Inequalities on a Number Line

A visual guide to open and closed circles, shading direction, and compound inequality graphs — with worked examples for every pattern.

7 min read

Inequalities on a Number Line

How to read, draw, and interpret every inequality type on a number line — from single rays to compound intervals and union graphs.

7 min read

Compound Inequalities: AND vs OR

A focused explanation of overlap logic for chained and split inequalities.

8 min read

Absolute Value Inequalities Explained

A practical explanation of translating absolute-value statements into linear inequalities.

9 min read

Inequalities Word Problems with Solutions

A guide for moving from English conditions to algebraic inequalities without losing the meaning of the problem.

6 min read

Inequality Rules: What Changes When You Multiply by Negative?

A concept-first explanation of the most important rule in one-variable inequality solving.

FAQ

Common questions about solving inequalities

What types of inequalities does this calculator solve?

The calculator solves linear, quadratic, absolute-value, rational, compound, and one-variable system inequalities, plus linear two-variable inequalities for coordinate-plane graphing. It explains the algebra and shows the matching graph.

Does the inequality calculator show steps?

Yes. Every supported inequality includes step-by-step reasoning so students can see how the expression is rearranged, where critical points come from, and why each interval is included or excluded.

Can I use the calculator for interval notation?

Yes. Every solution includes interval notation and set notation. If the answer is all real numbers or no solution, the calculator states that clearly.

When does the inequality sign flip?

The sign flips only when you multiply or divide both sides by a negative number. The calculator highlights that rule in the step list when it applies.

Does the calculator support graphing inequalities?

Yes. One-variable inequalities appear on an animated number line, and linear two-variable inequalities appear on a coordinate plane with a shaded half-plane and solid or dashed boundary line.

Is this inequality calculator free?

Yes. The core calculator, steps, graph, and notation outputs are free to use on desktop and mobile.

Can the calculator solve quadratic inequalities with two roots?

Yes. When a quadratic has two real roots, the calculator identifies the critical points, tests the intervals they create, and shows the final answer in both notation and graph form.

Can I share a solved inequality with someone else?

Yes. The current problem can be stored in the URL query string, so you can copy the link or the iframe embed code and send the exact same setup to students, teammates, or readers.

SEO Topics

Study paths people actually search for

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Inequality Calculator is an online inequality calculator for students who need more than a final answer. It works as a free inequality solver with steps for homework, revision, and classroom review, pairing algebraic moves with interval notation, graph output, and plain-language explanations. If you need a quick check, you can start with the linear inequality calculator. If you are studying graphs, the graphing inequalities calculator for teachers and learners makes shading, boundary style, and test points easier to verify.

The site also covers the longer-tail topics that usually appear in algebra practice and test prep: an interval notation calculator for algebra practice, a compound inequality calculator for test prep, a quadratic inequality calculator with graph, and a rational inequality calculator with sign chart. Because the layout is responsive, it also works well as a mobile inequality calculator for SAT and ACT prep when you are checking examples between classes. If you want guided explanations instead of only tool output, open the learning center, then follow the related calculator links or contact the team with a specific math-tool question.