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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