**Video Transcript**

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Transcript
**Inequalities and Their Graphs**

This is Timmy. Timmy is the best man at his friend's wedding, but he is running super late. The road he's driving on has a speed limit of 55 miles per hour, which means he should not drive more than 55 miles per hour. This can be represented by an inequality.

### Graphing Inequalities: x < y

Let's take a closer look, how to graph this **inequality on a number line**. The inequality representing speeds **less than** 55 mph is x < 55. To graph this on the number line, we draw an **open circle** at 55 mph and an **arrow to the left**, which shows all speeds less than 55mph.

However, Timmy could also drive at exactly 55 mph, which is the posted speed. The inequality representing speeds 55mph and under is: x is **less than or equal to** 55mph. We can show this on the number line by using a **closed circle** at 55 mph instead of an open one, along with the **arrow to the left** that represents all speeds less than 55mph. Our graph represents the speeds Timmy could drive.

And remember: we use a closed circle because 55mph is included in the inequality, since Timmy could drive at exactly 55mph.

### Graphing Inequalities: x > y

Timmy really has to hurry because he's got the wedding cake! Could he go faster than 55mph? Not without breaking the law and risking getting a speeding ticket for driving too fast. We can represent speeds that are faster than 55mph with the inequality x > 55.

The graph of this inequality has an **open circle** at 55mph and **arrow to the right**. This graph shows the speeds that would earn Timmy a speeding ticket, since all of them are faster than the posted speed limit.

### Graphing Inequalities: x > −y

Now that we understand the main idea of inequality graphs, let's look at another example. This inequality is x > −20.

To graph this, we must include all the numbers **greater than, but not equal to**, −20. Therefore, we draw an **open circle** at −20 and an **arrow to the right**.

If the inequality were x is **less than or equal to** −20, then we'd need to change two things on the graph.

First, −20 is included in the inequality, so we use a **closed circle**. Second, this inequality consists of numbers less than or equal to −20, so we use an **arrow to the left**.

Oh no! Even though Timmy obeyed the speed limit, he was in such a hurry that he didn't notice a bump in the road. Now the cake is ruined!