Inequality Calculator
Solve standard single-variable linear inequalities (e.g., ax + b < c). Features detailed steps showing operations and when to flip the inequality sign.
How to Use the Inequality Calculator
Interactive calculator available after JavaScript loads.
Loading calculator...
Math & Finance Experts — Verified Formulas, Peer-Reviewed Sources, Expert Analysis
Looking for a deeper explanation?
Read our comprehensive, peer-reviewed educational article in our Blog to learn the underlying math, formulas, and step-by-step examples.
Mathematical Formula & Logic
Step-by-Step Worked Calculation
Scenario: Solving a Negative Rate Inequality
Solve the inequality: -3x + 5 <= 17.
Step 1: Start with -3x + 5 <= 17.
Step 2: Subtract 5 from both sides: -3x <= 12.
Step 3: Divide by -3. CRITICAL: Because we are dividing by a negative number, flip the inequality sign: x >= 12 / -3.
Step 4: Simplify to get x >= -4. In interval notation, this is [-4, ∞).
How to Use the Inequality Calculator
- 1. Select your inequality operator (<, <=, >, >=).
- 2. Input the coefficients of your inequality (e.g., ax + b < c).
- 3. Check the simplified algebraic solutions, interval notations, and graph representation.
What Is a Inequality Calculator?
Inequality Calculator is a mathematical computation tool that helps you solve single-variable linear inequalities. Automatically flips signs when multiplying or dividing by negatives and shows interval notation. It applies established mathematical principles to deliver accurate results, often showing the underlying formula and step-by-step working so you can understand the computation process.
Why This Calculation Matters
Mathematical calculations form the foundation of science, engineering, finance, and everyday problem-solving. Inequality Calculator helps you work through calculations accurately and efficiently, reducing the risk of manual arithmetic errors. Whether you are a student learning concepts, a professional verifying work, or anyone needing quick and reliable math results, this tool ensures precision and saves time.
Historical Background
Mathematics has evolved over thousands of years, from ancient Babylonian clay tablets and Egyptian papyri to Greek formal proofs by Euclid and Archimedes. The development of algebra by Persian mathematician al-Khwarizmi in the 9th century and the invention of calculus by Newton and Leibniz in the 17th century laid the groundwork for modern computation. Inequality Calculator continues this tradition by making mathematical operations accessible through digital technology.
Frequently Asked Questions
Complete indexable directory of answers (6 questions)
When do you flip the inequality sign?
You must flip the inequality sign whenever you multiply or divide both sides of the inequality by a negative number.
What is the difference between open and closed intervals?
An open interval (using parentheses) does not include the boundary point. A closed interval (using brackets) includes the boundary point (e.g., <= or >=).
How do you represent infinity in interval notation?
Infinity (∞) and negative infinity (-∞) always use parentheses, never brackets, because they are boundaries that cannot be reached.
What mathematical formula does the Inequality Calculator use?
The Inequality Calculator uses standard mathematical formulas validated against authoritative references. The specific formula is displayed in the calculator interface with a detailed explanation of each variable.
How can I verify the Inequality Calculator results manually?
Each calculator includes a step-by-step worked example showing exactly how the formula is applied. You can follow these steps with pen and paper to verify any result.
What types of inputs does the Inequality Calculator accept?
The Inequality Calculator accepts numeric inputs including integers and decimals. Invalid inputs (letters, special characters) are rejected with clear error messages.