How to Graph Single–Variable Inequalities

by Reza about 2 years ago in Articles

You need to use a number line to graph single-variable inequalities. Learn how to graph an inequality with one variable.

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:

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

This image has an empty alt attribute; its file name is answer-3.png

Answers

1. \(\color{blue}{ – 2 > x }\)

2. \(\color{blue}{ x ≤ -5 }\)

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

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