State the interval that is represented by the following number line.
So the first thing that we can notice about our number line is the fact that we’ve got open circles. So we’ve got open circles and the blue line between them. Well an open circle means it’s not or equal to. So what that means is it doesn’t include the number that it’s on. So it doesn’t include the number four, and it doesn’t include the number two.
So therefore, we if we call our number 𝑥, we can say that 𝑥 must be greater than two because the line goes to the right of the circle on two but less than four. And this is because it goes to the left of the circle on four. And as we said it doesn’t include two and four because they’re open circles. If we wanted to include two and four, the circles would be colored in.
Well have we answered the question? We found the inequality that satisfies the number line that we have shown. Well no because it says in the question that we want to state the interval. So therefore, we need to use interval notation. So therefore, using interval notation, we can say that the interval notation for this number line will be two, four. And that’s inside parentheses.
The fact that we’re using parentheses shows that it’s open dots or not equal to. If we had closed dots, so we wanted to say that it was including that number, we’d in fact use brackets like this. So therefore, we can say that the interval that is represented by the following number line is two, four in parentheses.