Inequalities and Their Graphs 03:30 minutes

Video Transcript

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!