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

For Example:

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

We include all numbers less than 5 (to the left) and also shade the circle on 5 because it can equal 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:

is an equation because it is equal to a certain number.

In inequality, it doesn’t exactly equal to.

Examples of inequality are:

Or could be more complex like this:

So, how do we graph this inequality?

Let’s see how to graph the equation .

Draw a number line. The point that has is our equation .

Now, let’s look at the inequality

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

So, are all less than .

But so are .

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 . Then draw a line going to the left which represents the infinite numbers which are less than .

Let’s have more examples:

First, let’s draw a number line.

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

Now, let’s do .

Draw a number line.

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

Draw a number line.

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

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

has the same meaning as .

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

Likewise we can write as .

is also same as .

And can also be written as .