Online Inequality Calculator
Solve linear, quadratic, and rational inequalities from a photo or text.
Crop to the inequality
Step-by-Step Solution
Our Tools
Main Problem Solver
Solve problems in math, physics, chemistry, and more, just by taking a picture.
Perfect for Every Student's Journey
Whether you're struggling with your first algebra class or prepping for college entrance exams, our inequality solver adapts to your learning level and helps you build confidence step by step:
- Middle & High School Students: Master the fundamentals with clear explanations of sign charts, critical points, and interval notation that actually make sense.
- AP & College Students: Tackle advanced problems involving polynomial inequalities, exponential functions, and compound inequalities for Calculus readiness.
- Homeschool Parents: Become your child's math hero with detailed solutions you can explain confidently, even if algebra feels like ancient history.
- Test Prep Students: Boost your SAT, ACT, or GRE math scores with targeted practice on inequality problems that commonly appear on standardized tests.
From Problem to Solution in Under 60 Seconds
Stop wasting entire evenings on homework that should take minutes. Our advanced AI inequality calculator transforms frustrating algebra problems into clear, understandable solutions faster than you can say "quadratic formula":
- Multiple Input Methods: Upload photos of handwritten problems, type equations directly, or paste from digital textbooks—we handle messy handwriting and complex formatting.
- Smart Problem Recognition: Our AI instantly identifies whether you're dealing with linear, quadratic, rational, absolute value, or exponential inequalities and applies the most efficient solution method.
- Complete Step-by-Step Breakdowns: Every solution includes detailed work showing factoring, sign analysis, interval testing, and final answer verification with visual number line graphs.
- Error Prevention Tips: Learn common mistakes students make and how to avoid them, including domain restrictions and boundary point analysis.
Deep Understanding Beats Memorization Every Time
We believe in teaching the "why" behind every step, not just the "what." Our solutions go beyond basic answers to build genuine mathematical understanding that sticks with you through future courses:
- Conceptual Explanations: Understand why we flip inequality signs when multiplying by negatives and how to handle undefined points in rational expressions.
- Visual Learning Tools: See exactly where solutions exist on number lines with clear open/closed circle notation and interval shading that makes sense.
- Multiple Solution Methods: Learn various approaches like graphing, factoring, sign charts, and test point methods so you can choose what works best for you.
- Real-World Applications: Connect abstract algebra to practical scenarios like profit margins, speed limits, and optimization problems.
Master Every Type of Inequality Problem
From basic one-variable inequalities to complex multi-step systems, our calculator handles the complete spectrum of problems you'll encounter in middle school through college mathematics:
- Linear Inequalities: Master the basics like 3x + 7 > 2x - 1, including graphing solutions and understanding slope relationships.
- Quadratic Inequalities: Solve x² - 5x + 6 ≥ 0 using factoring, completing the square, or the quadratic formula with clear parabola visualization.
- Rational Inequalities: Handle complex fractions like (x-1)/(x+3) ≤ 2, including domain restrictions and vertical asymptote analysis.
- Absolute Value Inequalities: Break down |2x - 5| < 7 into cases and understand the geometric interpretation on coordinate planes.
- Polynomial Inequalities: Solve higher-degree problems like x³ - 4x² + x + 6 > 0 using sign analysis and graphing techniques.
- Exponential & Logarithmic Inequalities: Tackle 2^x > 8 and log(x+1) ≤ 3 with proper base conversions and domain considerations.
- Systems of Inequalities: Find intersections and unions of multiple inequality solutions with shaded region graphing.
- Compound Inequalities: Solve "and" and "or" problems like -3 < 2x + 1 ≤ 9 with clear interval notation.
Ace Your Tests with Confidence
Transform test anxiety into test confidence. Our inequality calculator doesn't just solve problems—it teaches you to think like a mathematician, preparing you for success on everything from pop quizzes to college entrance exams:
- SAT & ACT Preparation: Practice with problems modeled after real test questions, including time-saving shortcuts and common trap answers to avoid.
- AP Calculus Readiness: Build the strong inequality foundation you'll need for limits, derivatives, and optimization problems.
- College Placement Tests: Review essential skills to place into the right math course and avoid costly remedial classes.
- Final Exam Success: Use our tools for comprehensive review of semester-long inequality topics with targeted practice problems.
Real Success Stories from Students Like You
"I was completely lost on rational inequalities until I found this calculator. The step-by-step explanations finally made the interval method click for me. Just scored a 720 on my SAT math practice test!"
"Dude, this thing is a lifesaver! I went from failing every inequality quiz to actually understanding how sign charts work. My teacher asked what changed—I told her about this site and she was impressed with my improvement."
"As a homeschool parent, I needed help explaining why we flip inequality signs. This calculator's detailed explanations helped me teach my kids with confidence. We all learned something new!"
"I recommend this to my Algebra 2 and Pre-Calculus students for extra practice. The quality of explanations rivals what I provide in class, and students come back with much better understanding of complex rational inequalities."
"Perfect for checking my Calculus homework before submitting. The calculator catches my algebraic mistakes in inequality problems so I don't lose points on computational errors. Saved my GPA!"
"The advanced features helped me understand optimization problems for AP Calculus. Learning different solution methods here gave me multiple approaches to tackle tough exam questions. Definitely using this for AP prep!"
Your Questions Answered
Our calculator handles virtually every inequality type taught in middle school through college: linear inequalities (ax + b > 0), quadratic inequalities (ax² + bx + c ≥ 0), rational inequalities with fractions, absolute value inequalities, polynomial inequalities, exponential and logarithmic inequalities, systems of inequalities, and compound inequalities. We also solve word problems involving inequalities.
Our interactive number line shows exactly where your solutions exist with color-coded regions, open circles for excluded points, and closed circles for included points. You'll see sign changes at critical points, understand why certain intervals satisfy the inequality, and learn to read interval notation like (-∞, 3) ∪ (5, ∞) with confidence.
Absolutely! Our advanced OCR (optical character recognition) technology reads handwritten problems, textbook pages, and even poorly lit photos. Just make sure the mathematical symbols are clearly visible. We recognize standard notation including inequality symbols (>, <, ≥, ≤), fractions, exponents, and absolute value bars.
The domain determines which x-values are mathematically valid inputs. For rational inequalities, you can't have zero denominators. For square roots, you can't have negative numbers under the radical. For logarithms, you need positive arguments. Ignoring domain restrictions leads to incorrect solutions, so we always identify and explain these limitations first.
The inequality symbol tells you everything! Strict inequalities (> or <) use open circles because the endpoint isn't included in the solution. Non-strict inequalities (≥ or ≤) use closed circles because the endpoint is included. Additionally, any point that makes a denominator zero always gets an open circle since it's not in the domain, regardless of the inequality symbol.
Our calculator uses proven mathematical algorithms with 99.9% accuracy on standard algebra problems. Every solution includes verification steps where we test boundary points and intervals. However, we recommend using our tool as a learning aid alongside your textbook and teacher instruction, especially for high-stakes exams where showing your own work is required.
Definitely! Inequality problems appear frequently on standardized tests, often in word problem contexts or as part of larger algebraic manipulations. Our calculator helps you practice the types of problems you'll see, learn time-saving techniques, and build the foundational skills needed for advanced topics like optimization in AP Calculus.
Our calculator excels at translating word problems into mathematical inequalities. Whether you're dealing with budget constraints, speed limits, profit maximization, or temperature ranges, we show you how to set up the inequality, solve it step-by-step, and interpret the results in the context of the original problem.