- Writing, Graphing and Solving Inequalities
- Home
- Translating a Sentence by Using an Inequality Symbol
- Translating a Sentence into a One-Step Inequality
- Introduction to Identifying Solutions to an Inequality
- Writing an Inequality for a Real-World Situation
- Graphing a Linear Inequality on the Number Line
- Writing an Inequality Given a Graph on the Number Line
- Identifying Solutions to a One-Step Linear Inequality
- Additive Property of Inequality with Whole Numbers
- Multiplicative Property of Inequality with Whole Numbers
- Solving a Two-Step Linear Inequality with Whole Numbers
- Solving a Word Problem Using a One-Step Linear Inequality

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Writing an Inequality Given a Graph on the Number Line

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

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

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