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Modulus Inequalities Calculator Online

The Modulus Inequalities Calculator is a specialized tool designed to assist in solving modulus inequalities, which are mathematical expressions that involve the absolute value of variables. It offers a straightforward approach by automating the computation process, allowing users to input their inequality and instantly receive solutions.

Formula of Modulus Inequalities Calculator

To effectively use the Modulus Inequalities Calculator, one must understand the basic forms of modulus inequalities:

Type 1: |x| < a For inequalities where the absolute value of x is less than a, the solution is given by the range:

-a < x < a

Type 2: |x| > a For cases where the absolute value of x is greater than a, the solutions are not continuous and are found in two parts:

x < -a or x > a

These formulas are crucial as they form the foundation upon which the calculator operates, providing accurate and quick solutions.

Example of Modulus Inequalities Calculator

Consider the inequality |x – 3| < 7. Using the calculator, we input the expression and specify the type as ‘less than’. The calculator processes this to provide the solution:

-4 < x < 10

This example demonstrates the calculator’s utility in solving real-world problems quickly and efficiently.

Common Terms Table

This table serves as a quick reference for users unfamiliar with certain terms related to modulus inequalities.

Most Common FAQs

What is a modulus inequality?

A modulus inequality involves comparisons where one or both sides contain the absolute value of a variable.

How does the Inequalities Calculator work?

It simplifies the process of solving inequalities by automating the split and solution of the equation based on the specified type—either ‘less than’ or ‘greater than’.

Can the calculator handle complex inequalities?

Yes, the calculator is designed to handle both simple and complex modulus inequalities, providing reliable and accurate solutions.