Inequalities Calculator
Inequalities are a core part of algebra that describe the relationship between expressions using symbols like greater than (>), less than (<), or equal variations (≥, ≤). Whether you’re a student learning algebra or someone who needs quick inequality solutions, this Inequalities Calculator will make your task simple and accurate.
Our calculator handles multiple inequality types — linear inequalities, compound inequalities, and absolute value inequalities — providing not only the solution but also interval notation and a number line representation. This guide explains how to use the calculator and understand the outputs.
What Is an Inequalities Calculator?
It’s a tool designed to solve inequalities of various forms, including:
- Linear Inequalities: Expressions like ax + b > c
- Compound Inequalities: Expressions like a < x < b
- Absolute Value Inequalities: Expressions like |x| > a
Instead of manually rearranging and solving inequalities, simply enter coefficients, select inequality types, and get the solution instantly.
How to Use the Inequalities Calculator
Step 1: Enter Coefficients and Constants
- Coefficient (a): The constant term in the inequality (e.g., the b in ax + b > c).
- Variable Coefficient (b): Coefficient of the variable x. Default is 1 if you want to solve inequalities like x + a > c.
- Constant (c): The constant on the right side of the inequality.
Step 2: Select the Inequality Type
Choose from:
- Greater Than (>)
- Greater Than or Equal (≥)
- Less Than (<)
- Less Than or Equal (≤)
Step 3: Choose Inequality Form
- Linear: For inequalities involving ax + b and c.
- Compound: For inequalities where x is between two numbers (a < x < b).
- Absolute Value: For inequalities involving |x| and a.
Step 4: Calculate or Reset
Click Calculate to get the solution and detailed results. Use Reset to clear inputs and start over.
What Results Will You Get?
- Original Inequality: The inequality expression based on your inputs.
- Solution: The simplified inequality solving for x.
- Interval Notation: The range of values satisfying the inequality shown in interval form.
- Number Line: A simple text-based visualization showing the solution range on a number line.
- Test Value (x = 0): Checks if zero satisfies the inequality to help understand solution validity.
Example Usage
Suppose you want to solve:
2x + 3 > 7
- Enter Coefficient (a): 3
- Enter Variable Coefficient (b): 2
- Enter Constant (c): 7
- Inequality Type: Greater Than (>)
- Inequality Form: Linear
Hit Calculate, and you get:
- Solution: x > 2.0000
- Interval Notation: (2, ∞)
- Number Line: 2 ○―――→
- Test Value: 0 > 2 + 3 > 7 is FALSE (zero does not satisfy the inequality)
Why Use the Inequalities Calculator?
- Fast & Accurate: Get solutions without errors or manual steps.
- Supports Multiple Forms: Works for linear, compound, and absolute inequalities.
- Clear Visualization: Interval notation and number line help understand the solution.
- Educational: Great for students to verify homework and learn inequality solving.
Quick Tips
- Always input valid numeric values for coefficients and constants.
- Remember variable coefficient can’t be zero in linear inequalities.
- For compound inequalities, input limits for the range.
- Use the test value output to confirm if your guess value satisfies the inequality.
FAQs
1. What is a linear inequality?
An inequality where the variable appears with a power of one, like 2x + 3 > 7.
2. What is a compound inequality?
An inequality involving two comparisons combined, such as 1 < x ≤ 5.
3. How do absolute value inequalities work?
They involve expressions like |x| > a, meaning the distance of x from zero is greater than a.
4. Why does the inequality direction change when dividing by a negative number?
Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.
5. Can this calculator handle inequalities with zero coefficients?
No, the variable coefficient must be non-zero for linear inequalities.
6. What does interval notation mean?
A compact way to express all solutions, e.g., (2, ∞) means all numbers greater than 2.
7. How can I interpret the number line output?
It shows solution boundaries with open (○) or closed (●) circles indicating strict or inclusive inequalities.
8. What if I want to reset and start fresh?
Use the Reset button to clear all fields.
9. Can I use this for homework help?
Yes, it’s a useful tool to check your answers and learn solving steps.
10. Is this calculator free to use?
Yes, it’s designed to be accessible to everyone learning inequalities.
Conclusion
The Inequalities Calculator is a powerful yet simple tool that helps you solve various inequality problems with confidence. It supports multiple forms and provides clear, interpretable results with interval notation and number line visualization. Whether you’re studying algebra or need quick solutions, this calculator is your perfect assistant.
Try it out to solve inequalities quickly and understand their solutions deeply!