Inequalities are just equations with an "<" or ">" instead of "=". In this chapter, we'll look at how to solve a few different types of "linear" inequalities: ones with just X, where you present the answer in Interval Notation, and ones with X & Y, where you shade one side of the line or another. We'll also cover systems of inequalities, "and" vs "or", etc. For other types of inequalities, try this page.
This video is all about what to do when your quadratic "equation" suddenly has a "<" or ">" instead of an equals sign. Not surprisingly, to solve "quadratic inequalities" we'll use a fun combination of the "quadratic" methods from this chapter (factoring mostly) and solving inequalities stuff from the previous chapter.
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.
These videos cover a few theorems that all involve "inequalities". In previous chapters, you were always trying to prove two triangles or segments congruent. In this one, you're trying to prove things unequal, whether it's saying that one side in a particular triangle is longer than another side, or that a side in one triangle is longer than a side in another.
Not so different from the quadratic inequalities of the previous video, just more spots on number line! Plus, since there's more factors to play with (as your egghead teacher might say), they can pull some fun (their word) and/or mean tricks (mine) with exponents and repeated roots.
Absolute value signs (i.e. |x+3|) wreak havoc on equations and inequalities, often resulting in multiple answers and interval notation, but I'll give you simple steps to memorize for dealing with them. If you need to graph absolute value functions, check out thelibrary functions page.
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.
When you replace the "=" with a "<" or ">", unfortunately absolute value problems get a lot tougher. Or at least more complicated. These are fair game on the SAT, though, so gotta respect that. And the tricks I teach in this video seem to work for most students.
What happens when you put two polynomials above each other in an inequality? Believe it or not, it's not that much worse than if there was no fraction, just gotta be careful with open dots! (For a refresher on finding common denominators when x's and x2's are involved, check out my solving rational equations video.)
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.
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.
"Quadratic" means "squared", for some reason, so this chapter is about solving equations with x2's in them. You'll have to learn several tricky techniques -- square rooting, factoring, completing the square, and/or the Quadratic Formula -- but I give you tips to make them easier, and to decide which to use in different situations.
Absolute value equations are confusing when you see them, but they're not as bad as inequalities. Just get that absolute value alone on one side of the equations, then turn it into two separate equations as I explain in this video, and you'll never be the same.
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...)