Understanding Inequality Symbols and Graphing Compound Inequalities

This page provides a comprehensive overview of inequality symbols and how to graph compound inequalities on a number line. It covers the basic inequality symbols, their meanings, and how to represent them graphically.

The page begins by introducing the four main inequality symbols:

Vocabulary:

• Less than (<)
• Greater than (>)
• Less than or equal to (≤)
• Greater than or equal to (≥)

These symbols are fundamental in expressing mathematical relationships between quantities.

The guide then moves on to explain how to graph simple inequalities on a number line. It introduces the concept of open and closed circles:

Definition: An open circle (○) is used to represent a strict inequality (< or >), while a closed circle (●) represents an inclusive inequality (≤ or ≥).

Example: For the inequality x < 4, the graph would show an open circle at 4 on the number line, with an arrow extending to the left.

The page also covers compound inequalities, which combine two or more simple inequalities using "AND" or "OR" conditions:

Highlight: Compound inequalities with "OR" are represented by combining the graphs of individual inequalities, while "AND" inequalities show the overlap between two conditions.

Several examples are provided to illustrate these concepts:

1. x ≤ 3 OR x > 5: This is graphed with a closed circle at 3, an arrow extending left, and an open circle at 5 with an arrow extending right.
2. -3 < x ≤ 4: This "AND" inequality is graphed with an open circle at -3, a closed circle at 4, and a line connecting them.

The page concludes with a complex example showing multiple inequalities on a single number line, demonstrating how to represent various conditions simultaneously.

Vocabulary: Compound Inequality - An inequality that involves two or more conditions combined with "AND" or "OR" statements.

This comprehensive guide provides students with the tools to understand and graphically represent both simple and complex inequalities, enhancing their ability to solve and interpret mathematical problems involving inequalities.