Table of Contents

Introduction

Absolute Value

Compound Inequalities and the
Rapid Fire Method

Absolute Value Inequalities

More Absolute Value Inequalities:
The Greater Than Case

Absolute Value Equations

Absolute Value: Word Problems
and Applications

Introduction

In continuation of our Wiz Kid Algebracadabra series, we begin now our journey into Part II of this exciting exploration into short-cut algebraic methods and mastery of this subject. For those of you who read Part I, you saw how you could master and gain control over algebra problems by learning some fundamental methods within the Wiz Kid teaching philosophy. Techniques such as the Light Switch Property and the Bridge-Toll Method have given you a new sense of power over this seemingly difficult subject, which has thwarted the attempts of many students to come out ahead when navigating within this realm.

Now that you have the learned the fundamental terminology, and have mastered the methods for simplifying expressions, and solving both equations and inequalities, we can move into some more involved areas of algebra, where you will once again learn short-cuts toward mastery of this challenging discipline. With this task accomplished, you will be able to progress toward the higher reaches of mathematics including pre-calculus, calculus, and even analysis. Who knows? You might even end up a nuclear engineer or forensic pathologist. For all resides with math. Once you understand this concept, you will be so far ahead of the pack that you won’t know what to do with yourself.  And don’t worry if people think you’re a math nerd because, in all likelihood, they’ll just be jealous that you have mastered a subject that has kicked enough butt to qualify for a murder sentence.

Here we’re going to examine such concepts as absolute value: that nasty double-edged sword that daunts the ablest of students. We will slay compound inequalities as though they were ice cubes facing a scorching sun. Combining the previous two concepts, we will then move into mastery of absolute value inequalities, a not too shabby feat. After having kicked some butt in this area, we will then go onto the galleries where lines reside. We will master any and all problems involving lines and their associates: slope, intercepts, and equations.

As if the above were not enough, we will learn to master the quadratic equation, that ever devious creation of two wicked parents, whose aim was to destroy algebra students across the globe. Need I add that you will even learn to understand the way in which the famous quadratic equation is derived. Wow! I’m getting excited just writing about this stuff. Oh and by the way. When you bring the A’s home to your parents and you hand them your report card, while standing there smugly, observe how they glimmer with glee, ready to hand you the keys to the universe. Okay, so I'm exaggerating a little. But really, you will be happy with the results. So let’s get going so you can reap the benefits of what algebra mastery can give you.

Absolute value, never negative we’re told,
But insert a variable and I've lost my hold.
It's x.no it’s negative x, c’mon what’s the deal?
I must be dreaming, this can’t be real!
Help, please help teacher, help me to feel.

Taken from the poem Help, Please Help Teacher from the collection Poems for the Mathematically Insecure

As the above stanza of the poem Help, Please Help Teacher shows, absolute value can be a real nightmare for students. The main reason for this is that absolute value can mean more than one thing, and anytime a concept.particularly in math. that can mean more than one thing, you have a
problem. The absolute value of a number or expression is written using the symbol "|  |", the expression or number being placed within. For example, the absolute value of 3 is written as |3|. The absolute value of x is |x|. The absolute value of an expression or number is always positive and this idea has a geometric interpretation. The absolute value of a number is that number’s distance to 0 on a number line. For example the absolute value of 8 is |8| = 8 because 8 is 8 units away from 0. Common sense. Nothing fancy here. Just look at the number line.

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