Visual representation of inequalities on a number line is an essential skill in algebra, facilitating a deeper understanding of mathematical concepts and solution sets.

Introduction

Representing inequalities on a number line enables students to visually grasp the range of values that variables can take, making abstract concepts more tangible.

Symbols and Their Meanings

• < and >: Indicate values less than or greater than a number, excluding the number itself.
• ≤ and ≥: Indicate values less than or equal to, or greater than or equal to a number, including the number itself.

Representation Techniques

Open and Closed Circles

• Open Circle: Used for "<" and ">", showing that the endpoint is not included.
• Closed Circle: Used for "≤" and "≥", showing that the endpoint is included.

Image courtesy of  My World Is My Classroom

Example:

Represent the compound inequality -4 ≤ x &lt; 2 on a number line, indicating the range of values x can take.

Steps

1. Draw the Number Line: Start with a horizontal line and mark points for -4 and 2.
2. Mark -4 with a Closed Circle: Since -4 is included in the range (indicated by "≤"), we use a closed circle at -4.
3. Mark 1 with an Open Circle: Since 1 is not included in the range (indicated by "<"), we use an open circle at 2.
4. Shade the Region Between -4 and 2: This shading represents all values of x that satisfy the inequality, indicating that x can be any value between -4 and just below 2.

Practice Problems

To master representing inequalities on a number line, practice with a variety of inequalities, focusing on where to place open and closed circles and how to shade the number line correctly.

Problem 1: Represent x &gt; 2

• Mark an open circle at 2 and shade to the right, indicating all values greater than 2.

Problem 2: Represent $x ≥ -1$

• Mark a closed circle at -1 and shade to the right, including -1 and all values greater than -1.