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

Term | Description |
---|---|

Absolute Value | The distance of a number from zero on the number line, without considering direction. |

Inequality | A mathematical statement that indicates the relative size or order of two values. |

Modulus | Another term for absolute value. |

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.