### Video Transcript

The situation where 𝑥 has to be at least
two away from one can be expressed by the compound inequality 𝑥 minus one is less than
negative two or 𝑥 minus one is greater than two. Which of the following number lines
represents this inequality?

Well, the first thing we need to look at
with this question is this wording here, compound inequality. Well, what is a compound inequality? Well, it’s an inequality that has two or
more inequalities joined together with either “and” or “or,” like we have here in this
question. So, in this problem, our compound
inequality has two parts. So, we deal with the left-hand part
first, which is 𝑥 minus one is less than negative two.

Well, what we want to do is we want to
solve this in the same way that we’d solve an equation. So, we’re gonna add one to each side of
our inequality. So, this is gonna give us 𝑥 is less than
negative one. Okay, so, that’s the first part of our
compound inequality solved. So, we know what our 𝑥-value or our
𝑥-region is gonna be first, and that is 𝑥 less than negative one. So, for the second part of our compound
inequality, we have 𝑥 minus one is greater than two.

So, again, once more, what we do is we
add one to each side of the inequality to solve. So, we get 𝑥 is greater than three. So, if we put that together, what we get
is that 𝑥 is less than negative one or 𝑥 is greater than three. It’s not a double inequality because
we’re not looking for a region between two values. So, we’ve actually got two separate parts
to our compound inequality. And if we think about our number-line
inequality, we’re gonna have two open circles and one with an arrow to the left and one with
an arrow to the right. And this is because we haven’t got or
equal to.

So, therefore, if we look at our possible
answers, we can see that answer (D) is gonna be the correct one. Because we’ve got an open circle in the
line to the left at negative one. And we’ve got an open circle on the line
to the right at three. And we rule out answer (A) because it’s
got two closed circles and answers (B) and (C) because they represent regions between two
values.