Video Transcript
Which of the following diagrams
represents the inequality 𝑥 is greater than or equal to negative two but less than one?
So, if we take a look at the inequality
we have in this question, we can see that it’s a double inequality because we’ve got two
inequality signs. And that is, it is an amalgamation of the
two inequalities 𝑥 is greater than or equal to negative two and 𝑥 is less than one. And what this is gonna show is a region
between two values. So, if we’re gonna want to represent this
on a number line, what we need to do is remind ourselves of some of the notation we use.
So, if we take a look at the first
inequality sign, we’ve got 𝑥 is greater than or equal to negative two. So, therefore, because it’s greater than
or equal to, we’re gonna have a colored-in circle or dot in the line to the right because
the colored-in circle or dot means or equal to rather than just that value. And then, the line to the right is gonna
be greater than. Then, for the second part of our
inequality, we’re gonna have an open circle. And that’s because it’s just 𝑥 is less
than one. It’s not 𝑥 is less than or equal to
one. And then we’re gonna have a line going
off to the left because it’s less than. As we’d already said, this is a double
inequality. So, it represent a region between two
values. So, therefore, we’re gonna join the lines
between our two dots or circles.
So, now, we’ve got something that looks
like what we want. Well, we’re gonna represent our
inequality on a number line. And we can also see that our colored
circle is gonna be on the negative two. And the open circle is gonna be on the
one. So, if we take a look at our possible
answers, we can see that this is the same as answer (A). Because in answer (A), we have a
colored-in circle on the negative two and an open circle on the one. So, what this shows is that 𝑥 can be any
value between negative two and one which includes negative two, but doesn’t include one.
So, therefore, we can say that the
diagram which represents the inequality 𝑥 is greater than or equal to negative two but less
than one is diagram (A). And the other ones are incorrect for
various reasons involving the number-line notation. So, (B) has the incorrect dot colored in
and the incorrect dot open. In (C), they’re both colored in, and in
(D), they’re both open, which will be all incorrect.
