Writing an Inequality Given a Graph on the Number Line

Introduction

In this lesson, given a graph on the number line, we write an inequality for the graph.

Rules to write an inequality given a graph on the number line.

For any variable x

• If the graph is a horizontal line starting from a point a with an open circle and an arrow towards left, it is a less than inequality. x < a

• If the graph is a horizontal line starting from a point a with a closed circle and an arrow towards left, it is a less than or equal to inequality. x ≤ a

• If the graph is a horizontal line starting from a point a with an open circle and an arrow towards right, it is a greater than inequality. x > a

• If the graph is a horizontal line starting from a point a with a closed circle and an arrow towards right, it is a greater than or equal to inequality. x ≥ a

Example 1

Write an inequality for the graph on the number line given below.

Solution

Step 1:

From the given graph on the number line since the arrow is towards left and there is an open circle, it is a less than inequality.

Step 2:

Since it is starting from 190 with an open circle, the inequality is x < 190

Example 2

Write an inequality for the graph on the number line given below

Solution

Step 1:

From the given graph on the number line since the arrow is towards left and there is a closed circle, it is less than or equal to inequality.

Step 2:

Since it is starting from 15 with a closed circle, the inequality is x ≤ 15