Video Transcript
Find the solution set of the
inequality 𝑥 is less than or equal to 20 in the real numbers. Give your answer in interval
notation.
Now, I said this automatically when
reading the question, but the first thing to remember is that the inequality
notation that’s been used here is a “less than or equal to” sign. So this inequality tells us that
the value of 𝑥 is less than or equal to 20. This is known as a simple
inequality as there is only one inequality sign involved. And actually, this inequality has
already been solved for us as we have 𝑥 on its own on one side of the
inequality. Picturing a number line, we know
then that 𝑥 can take any value at all from 20 all the way down to negative ∞.
We can write this as an interval
with negative ∞ and 20 as its endpoints. But we must be careful about the
type of brackets or parentheses that we use at each end of the interval. As 𝑥 is less than or equal to 20,
20 is included in the possible values for 𝑥. So it is included in the solution
set, which means our interval needs to be closed at its upper end. However, as negative ∞ does not
exist as an actual number, our interval needs to be open at its lower end. We therefore have the solution set
of this inequality in interval notation. It’s the interval from negative ∞
to 20, which is open at the lower end and closed at the upper end.
