Introduction to Linear Inequalities

Learn inequality notation and concepts. Grade 9 Alberta mathematics curriculum.

Lesson 6.3 of Linear Equations & Inequalities in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• What Are Inequalities?. Learn what inequalities are, how they differ from equations, and the symbols we use to represent them.
• Writing Inequalities to Describe Situations. Translate real-world situations into mathematical inequalities by defining variables and using the correct symbols.
• Determining Solutions of Inequalities. Understand what makes a number a solution of an inequality by testing values to see if they make the statement true.
• Graphing Inequalities on a Number Line. Show the range of possible solutions on a number line using open and closed dots and shaded regions.
• Reading Number Line Graphs. Interpret inequalities from number-line graphs by identifying which direction is shaded and whether endpoints are included.

Inside the lesson — a free preview

What is an Inequality?

An inequality shows a relationship between two expressions that are not equal, using symbols like:

An equation has =, while an inequality uses one of these comparison symbols to describe a range of possible values instead of just one.

Key Idea

Understanding the Difference. An inequality doesn't always have one exact answer — it represents many possible values that make the statement true.

Instead of finding a single value, we often describe or show all the values that fit.

Types of Inequalities

Strict vs Non-Strict Inequalities. Strict inequalities (< and >) do not include the boundary value.

Non-strict inequalities (≤ and ≥) include the boundary value.

How to Write an Inequality

An inequality helps describe a range of possible values that satisfy a real-world condition.

To write one:

Key Strategy for Word Problems

Step-by-Step Process. Follow these steps when writing inequalities from word problems:

Important Tip

Understanding Inclusive vs Exclusive. When writing inequalities, pay attention to whether the number is included or not:

Equations vs. Inequalities

A linear equation is true for only one value of the variable. A linear inequality, however, can be true for many values of the variable.

Linear Equation: x + 3 = 8 ⇒ x = 5

There's only one value that makes the equation true.

Linear Inequality: x < 8

is true for 7, 6, 0, −2, and infinitely more values.

Worked example: Comparing Values

Testing Inequality Statements. Let's check if these inequality statements are true or false:

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