# Graphing Single–Variable Inequalities

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.

### 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.

### 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.

### Example 3:

Graph this inequality. $$x<5$$

Solution:

## Exercises

### Draw a graph for each inequality.

1. $$\color{blue}{– 2 > x}$$

2. $$\color{blue}{x ≤ – 5}$$

3. $$\color{blue}{x > 7}$$

4. $$\\ \color{blue}{1.5 > x}$$

## Answers

1. $$\color{blue}{ – 2 > x }$$

2. $$\color{blue}{ x ≤ -5 }$$

3. $$\color{blue}{ x > 7 }$$

4. $$\color{blue}{ -1.5 > x }$$