Question Video: Identifying the Linear Inequality Represented on a Given Number Line

What inequality is represented on the given figure.

02:18

Video Transcript

What inequality is expressed on the given figure.

On this figure, we have two ends points that are circles which are not filled in. When we’re dealing with inequalities, the end points tell us something. If the circle is not filled in, that value is not included. If the circle is filled in, that value is included. That means we can say that our values are all the values between negative four and two but does not include negative four or two.

We can use a variable to help us express this inequality. If we chose 𝑥, the line 𝑥 is greater than negative four would look like this. And the line 𝑥 is less than two would look like this. But our value falls between negative four and two. So how do we write this? We want to say that 𝑥 is greater than negative four and 𝑥 is less than two. We do this by putting our variable in the middle. We now have a statement that says negative four is less than 𝑥. And that’s the same thing as saying 𝑥 is greater than negative four. From there, we add that 𝑥 is less than two, and we’ve combined the two inequalities we started with.

Remember that if these circles were filled in, then our inequalities would be greater than or equal to or less than or equal to. But since they weren’t, we just have greater than or less than without the equal to part. There are a few different ways people might read this statement. You can say negative four is less than 𝑥 which is less than two. Or you could say that 𝑥 is between negative four and two. You could also say 𝑥 is greater than negative four and 𝑥 is less than two. That’s three different ways to read the same inequality. Negative four is less than 𝑥 which is less than two. And that’s the values represented on the given figure.

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