So, this is the solution set for our compound inequality. If you got it right,
nice work. If we stack the number lines on top of each other, like this, we can
see that there's a region of intersection. These are the numbers that are shared
between the inequalities. They make both of the inequalities true. And this is
why we learned about intersections, and really helps us figure out what numbers
make both inequalities true. We can see this region of intersection on one
number line. This is the solution set. We can also write it in interval
notation. So, notice that an and compound inequality makes an intersection, or a
region between points. And any of these numbers would work in both inequalities.
Let's check that out real quick. Let's check 6. We're going to let x equal 6 and
check the solution. So, plugging in 6, I get 7 less than or equal to 9 and
plugging in 6 over here, I get negative 8 is less than or equal to negative 7.
Both of these statements are true. So, that means 6 is a solution to this
compound inequality. Notice that for equations and inequalities, we've always
been able to check our answer. This is what so great, we can know that we're
right. Checking your answer can build your confidence in knowing that you're
right. Or it means, hey, maybe I should go back and check my work.
