Video Transcript
What inequality is expressed on the
given figure.
On this figure, we have two ends
points that are circles which are not filled in. When we’re dealing with
inequalities, the end points tell us something. If the circle is not filled in,
that value is not included. If the circle is filled in, that
value is included. That means we can say that our
values are all the values between negative four and two but does not include
negative four or two.
We can use a variable to help us
express this inequality. If we chose 𝑥, the line 𝑥 is
greater than negative four would look like this. And the line 𝑥 is less than two
would look like this. But our value falls between
negative four and two. So how do we write this? We want to say that 𝑥 is greater
than negative four and 𝑥 is less than two. We do this by putting our variable
in the middle. We now have a statement that says
negative four is less than 𝑥. And that’s the same thing as saying
𝑥 is greater than negative four. From there, we add that 𝑥 is less
than two, and we’ve combined the two inequalities we started with.
Remember that if these circles were
filled in, then our inequalities would be greater than or equal to or less than or
equal to. But since they weren’t, we just
have greater than or less than without the equal to part. There are a few different ways
people might read this statement. You can say negative four is less
than 𝑥 which is less than two. Or you could say that 𝑥 is between
negative four and two. You could also say 𝑥 is greater
than negative four and 𝑥 is less than two. That’s three different ways to read
the same inequality. Negative four is less than 𝑥 which
is less than two. And that’s the values represented
on the given figure.
