Inequality in Mathematics

An inequality is a mathematical statement that compares the values of two expressions using inequality symbols such as <, >, ≤, or ≥.

Types of Inequalities

Linear Inequalities: These are inequalities that involve linear functions and are represented on the coordinate plane as lines or half-planes.
Absolute Value Inequalities: These involve the absolute value of a variable and can be solved using the properties of absolute value.
Quadratic Inequalities: These involve quadratic functions and can be solved using methods such as graphing, factoring, or the quadratic formula.

Notation for Inequalities

Inequalities are typically expressed using the following notation:

Solving Inequalities

To solve an inequality, follow these general steps:

Isolate the variable: Use inverse operations to get the variable on one side of the inequality.
Identify the solution set: Determine the range of values for the variable that satisfy the inequality.
Graph the solution: Represent the solution set on a number line or coordinate plane.

Study Guide

When studying inequalities, it's important to understand the properties of inequalities and how to solve them. Here are some key concepts to focus on:

Understanding the meaning of the inequality symbols (<, >, ≤, ≥)
Identifying the solution set for an inequality
Graphing inequalities on a number line or coordinate plane
Solving linear, absolute value, and quadratic inequalities using appropriate methods

Practice solving a variety of inequality problems to reinforce your understanding of the topic. Pay attention to any special cases or rules that apply to specific types of inequalities.

Remember to check your solutions by substituting the values back into the original inequality to ensure they satisfy the given conditions.

Good luck with your study of inequalities!