Unit+6

Unit 6



In Unit 6 we begin an exploration of Inequalities and Absolute Values!!! Section Section 6-1 introduces the concept of inequalities to us by comparing them to the standard old-fashioned equations that we'd been working with for months. Inequalities are nothing more than equations with restrictions. Remember that an equal sign (which we find in equations) tells us that there is only one solution that can possibly make our math sentence true. (When you get into Algebra II you will learn that some equations have more than one solution, but for the time being you only need to know that linear equations only have one solution).

Inequalities, however, are expressions of two quantities which are not equal, but one is bigger or smaller than the other. This opens our possible solutions to many numbers.

We solve inequalities much like we do equations. There is one caveat---> *** Check out my notes on section 6-1 and 6-2 to find out** * Click to get them. Graphing the solutions to inequalities requires a number line. Remember that some solutions have open circles and some have closed circles. Do you know which is which?

When we stick two inequalities together and solve them simultaneously, we call them "compound inequalities". That is the subject of section 6-3. Compound inequalities are solved just like all other inequalities, but both solutions are graphed on the same number line.

The classwork and homework for this section can be found here if you click on the link-->

When you solve compound inequalities, there are two ways to do it: 1. Together 2. Separated into two inequalities

About half of you will do them together, and the other half will prefer separating them. It doesn't matter. If you decide to separate them, then you need to know the difference between an "and statement" and and "or statement". My notes on Section 6-3 explain the difference. You can download them and read them.

In Section 6-4 we returned to our good ol' friend absolute-value. In previous units we just talked about what absolute-value was, this time, we actually get to use it in equations and inequalities. We also talked about **transformations** of the **parent function y=|x|.**

**Remember transformations can come in four different types:** **1. Horizontal shift.** **2. Vertical shift.** **3. Change in slope. (sometimes called compression or stretch)** **4. Reflection across the x-axis.**

**You should be able to identify if our parent function has a transformation and what type just by looking at the equation. If you need some more explanation, check out my notes on that section .**



The last thing we did in Unit 6 was to solve equations and inequalities with absolute-value. I stressed over and over the importance of thinking of the absolute value as the distance from zero on the number line. That would help you figure out how to solve equations and inequalities. Remember that for each absolute-value equation and inequality there are 2 cases. You must find both and solve both to get a complete answer. My notes for that section can be found here.

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