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 < 2 on a number line, indicating the range of values x can take.

**Steps**

**Draw the Number Line**: Start with a horizontal line and mark points for -4 and 2.**Mark -4 with a Closed Circle**: Since -4 is included in the range (indicated by "≤"), we use a closed circle at -4.**Mark 1 with an Open Circle**: Since 1 is not included in the range (indicated by "<"), we use an open circle at 2.**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 > 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.