Learn How To Graph Inequalities On A Number Line

In this video, we will be learning how to graph inequalities without using the graphing calculator.

Example of Graphing Inequalities

$x = 5$

$x \textless 5$
Here, we include all numbers less than 5 (to the left), but do not shade the circle on 5 because it cannot equal 5.

$x \textgreater 5$
Here, we include all numbers greater than 5 (to the right), but do not shade the circle on 5 because it cannot equal 5.

$x \leq 5$
We include all numbers less than 5 (to the left) and also shade the circle on 5 because it can equal 5.

$x \geq 5$
Here, we include all numbers greater than 5 (to the right) and also shade the circle on 5 because it can equal 5.

Video-Lesson Transcript

Let’s go over how to graph inequalities.

First of all, what is inequality?

Look at this:

$x = 5$ is an equation because it is equal to a certain number.

In inequality, it doesn’t exactly equal to.

Examples of inequality are:

$x \textless 5$ $x \textgreater 5$ $x \leq 5$ $x \geq 5$

Or could be more complex like this:

$x + 7 \textless 5$

So, how do we graph this inequality?

Let’s see how to graph the equation $x = 5$ .

Draw a number line. The point that has $5$ is our equation $x = 5$ .

Now, let’s look at the inequality

$x \textless 5$

Here, we have an infinite number of solutions. Because we can have any number that’s less than $5$ .

So, $1, 2, 3, 4$ are all less than $5$ .

But so are $4.9, 4.2, -3$ .

There are infinite numbers.

Now, let’s graph this.

Draw a number line.

The equation has a point that represents the equals sign.

In inequality, we will just encircle the endpoint. In this case, it’s $5$ . Then draw a line going to the left which represents the infinite numbers which are less than $5$ .

Let’s have more examples:

$x \leq 5$

First, let’s draw a number line.

$x$ can be equal to $5$ so we can draw a point on it. Then let’s draw a line to the left which represents all numbers less than $5$ .

Now, let’s do $x \textgreater 5$ .

Draw a number line.

Let’s encircle the number $5$ and draw a line to the right which represents all numbers greater than $5$ .

$x \geq 5$

Draw a number line.

Highlight the point in number $5$ and draw a line to the right which represents all numbers greater than $5$ .

The line below the less or greater than sign means equal to.

$x \leq 5$ has the same meaning as $5 \geq x$ .

Think of the $\textless$ sign as a mouth. It’s going to eat whatever is bigger.

Likewise we can write $x \textless 5$ as $5 \textgreater x$ .

$x \geq 5$ is also same as $5 \leq 5$ .

And $x \textgreater 5$ can also be written as $5 \textless x$

After you finish this lesson, view all of our Algebra 1 lessons and practice problems.