Video: Graphing Linear Inequalities

Which inequality is represented on this number line?

01:28

Video Transcript

Which inequality is represented on this number line?

So, first of all, what we can see on our number line is we’ve got an arrow pointing to right. So, this means that we’re gonna be involving greater than. That’s because anything to the right of a value on a number line is greater than that value. Then, next, what we do is we remind ourselves of our number-line notation. And with our number-line notation, if we have an open circle and a line to the right, it’s greater than. But if we have a closed or colored-in circle and a line to the right or an arrow to the right, then it is greater than or equal to. And we can see in our diagram that it is colored in. So, therefore, it’s gonna be greater than or equal to.

So, what this means is, if we’ve got the colored-in dot, like we do in ours, then it’s gonna be greater than or equal to. So, it means it can take the value, so in this case, the value of the negative one cause if it was an open circle, it wouldn’t take this value as well. So, therefore, in word form, we can say that 𝑥 is greater than or equal to negative one.

However, we want to represent it using inequality notation. So, how would we do this? So, using our inequality notation, we have 𝑥 is greater than or equal to negative one. And we know it’s greater than because we’ve got the open side by the 𝑥 and the pointy side by the negative one. So, it’s 𝑥 is greater than negative one. And we know that it’s or equal to because this line underneath our inequality sign. So, we’ve got 𝑥 is greater than or equal to negative one.