Consider the following two inequalities. 𝐴 is greater than or equal to seven but less than or equal to 42. 𝐵 is greater than seven but less than 42. How do the integer values of 𝐴 and 𝐵 differ?
So let’s consider what’s different about the two statements or the two inequalities. So we’ve got the difference shown here. And it’s in the inequality notation that we’re using. And I’ve shown it using a couple of number lines.
So for the top number line, I’ve got 𝐴. I’ve got seven and 42. But above each of these, I’ve got closed dots, whereas for 𝐵, we’ve got open dots. And this is because of the signs, because we’ve got in 𝐴 that it is greater than or equal to or less than or equal to and in 𝐵 it is greater than or less than. So the closed dot means that it includes that number itself, so includes seven, includes 42, whereas the open dot means that it does not.
So therefore, we can say that the way that the integer values of 𝐴 and 𝐵 differ is that the integer values of 𝐴 include seven and 42. And we’ve shown that on our number line with the closed dots. But also it’s in our inequality notation because we can see that we’ve got a line underneath as well, whereas the integer values of 𝐵 do not include seven and 42. And again, we’ve shown that on our number line with our open dots. And we can see that in our inequality notation because there is not a line underneath.
So if we think about what this would mean in real terms, it would mean that 𝐴 would be equal to the values from seven, eight, then all the way up to 41 and 42, whereas the values for 𝐵 would start at eight and will go all the way up to 41.