How to Graph Single–Variable Inequalities? (+FREE Worksheet!)

Related Topics

• How to Solve One-Step Equations
• How to Solve Multi-Step Equations
• How to Solve One-Step Inequalities
• How to Solve Multi-Step Inequalities
• How to Solve Systems of Equations

Step by step guide to graphing single–variable inequalities

• Inequality is similar to equations and uses symbols for “less than” (\(<\)) and “greater than” (\(>\)).
• To solve inequalities, we need to isolate the variable. (like in equations)
• To graph an inequality, find the value of the inequality on the number line.
• For less than or greater than draw open circle on the value of the variable.
• If there is an equal sign too, then use filled circle.
• Draw a line to the right or to the left for greater or less than.

Graphing Single–Variable Inequalities – Example 1:

Draw a graph for \(x \ > \ 4 \).

Solution:

Since the variable is greater than \(4\), then we need to find \(4\) and draw an open circle above it. Then, draw a line to the right.

Graphing Single–Variable Inequalities – Example 2:

Draw a graph for \(x>2\).

Solution:

Since the variable is greater than \(2\), then we need to find \(2\) and draw an open circle above it. Then, draw a line to the right.

Graphing Single–Variable Inequalities – Example 3:

Graph this inequality \(x<5\).

Solution:

Since the variable is less than \(5\), then we need to find \(5\) and draw an open circle above it. Then, draw a line to the left.

Exercises for Graphing Single–Variable Inequalities

Draw a graph for each inequality.

1. \(\color{blue}{– 2 > x}\)

2. \( \color{blue}{x ≤ – 5}\)

3. \( \color{blue}{x > 7}\)

4. \(\\ \color{blue}{-1.5 > x}\)

Download Graphing Single–Variable Inequalities Worksheet

Answers

1. \(\color{blue}{ – 2 > x }\)

2. \(\color{blue}{ x ≤ -5 }\)

3. \(\color{blue}{ x > 7 }\)

4. \(\color{blue}{ -1.5 > x }\)