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Graphing Inequalities

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

For Example:

 x = 5

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.

xless5

 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.

xgreat5

 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.

xleq5

 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.

xgeq5

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.

Graphing Inequalities

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.