There are two types of inequalities: one-dimensional ones with just x where you graph the answer on a number line, and two-dimensional ones with both x and y where you graph a line and shade in one side of it. Most books and teachers put these two types of problems in two separate chapters, but in my tutoring experience it's best to teach them both at the same time so that students can see the differences up close and figure out how to tell them apart. That's key on a midterm or final when you'll see both types of inequalities on one test!
Solving Inequalities with just X
In this video we'll solve problems like 3x+4<7 and x-2>2. What do these problems have in common? Just X, no Y! So when we graph the answer, we'll do that on a number line. I also discuss the exciting topic of how to decide whether to use an "open" or "closed" dot.
Rather than write x > 5 or -2 < x < 4, we're going to put the numbers in parentheses and brackets, like (2,6) or [-3,1). The only trick: whether to use ( )'s or [ ]'s or some combination of the two! You'll also have to learn how to draw the infinity symbol super-good (lol).
Systems of Inequalities (with just X)
In this video we're given two inequalities aka compound inequalities instead of just one. We'll put them on the same number line, then decide how to do "and" vs "or". We'll then write the answer in interval notation, since we're crazy about that.
Linear Inequalities with both X & Y
Finally, those problems where you have to color in one side of a line! I didn't mention these earlier because I didn't want to get anyone excited, but this is definitely as good as this chapter is going to get. It's all downhill from here.
Systems of Inequalities with both X & Y
Systems, by now you've learned, means "two equations at once." And we get to color in one side of two lines at the same time! I know I said the chapter peaked last video, but this really is the best-best-best of inequalities. A key skill in linear programming.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)