Study Guide

Equations and Inequalities

Equations and Inequalities Introduction

The word algebra comes from the Arabic phrase al-jebr, meaning "the reunion of broken parts." Like your high school reunion will be if you go on to become a linebacker.

Besides being a mathy sort of word, around the 1500s or so, algebra was also used to mean "bonesetting." (The linebacker analogy still applies). Spanish still uses algebra that way, and algebrista in Spanish means "bonesetter." You thought this was a math class. Mwa-ha-ha-ha. That was our evil laugh. Yes, we've been practicing.

Algebra, as taught in schools today, has two main parts:

  1. Translating real-world problems into symbols, and 
  2. Manipulating the symbols to find answers.

This second one is nice, because it means a lot of problems can be broken down into two smaller ones that are easier to solve individually. Hey, we like "easier." First, we translate the problem into the language of math, and then we do some arithmetic and manipulation of symbols to find an answer. In other words, we manhandle those symbols. We show them no mercy. Oh yeah, we also need to remember to answer the right question while we're at it. Test-graders are real sticklers for accuracy, for some reason.

In this section we deal mostly with manipulating/manhandling symbols, but we also start tossing in problems that let us practice translating questions from English into math. (Just be grateful you don't need to translate War and Peace into math. Can you imagine how complicated that formula would be?) The translation stage is where we turn words into equations or inequalities. Then we manipulate symbols to solve the equations or inequalities, and find an answer.

We prefer answers because answers are the cat's pajamas. Equations and inequalities are the cat's hiking boots, at best.

But hold on—sometimes we don't get any answers, and sometimes we get more than one. The nice thing is that no matter how many answers there are, we'll know when we're done. Often, we can even check our answer(s) to make sure we're right. Might not be a bad thing to do before sending texts, too. It's time to stop blaming everything on AutoCorrect.

Equations and Inequalities Resources

Websites

Mathdrills.com: Algebra Worksheets
Plenty of helpful worksheets here, where you can get practice filling in missing numbers, rewriting formulas, and simplifying and evaluating algebraic equations. It’s not nearly as painful as the term "drill" implies.

Passy’s World of Mathematics: Equivalent Equations
One of the most important equation skills you’ll need to have in your repertoire is the ability to scale them up or down, depending on what's needed in any given situation. This site breaks down how to tell if two equations are equivalent, as well as how to create equivalent equations when necessary. It's like being able to identify identical twins in real life, assuming one of them has been exposed to nuclear radiation and has grown to three times his original size.

Video

Solving Algebraic Equations
It's important to always remember that whatever you do to the left side of an equation, you also need to do to the right side. This video will hammer that point home. Gee whiz— hammers, drills...who knew there was so much overlap between the skills of a mathematician and those of a handyman?

Khanacademy.org: Solving Inequalities
For more on solving inequalities and depicting them on a number line, watch this video from Khan Academy. For added fun, use your arrow and try to keep up with the arrow on the screen. Good luck.

Games and Tools

Mathplay.com: Hoop Shoot
This super-fun game combines equation-solving skills and basketball three-pointing skills. Okay, so they probably won’t translate to the court. Still, it is nice seeing that ball go "swish," even if it doesn’t earn you any jock points.

Mathplay.com: Inequality Game
Make the genie proud and pass this inequality quiz with flying colors. If you fail, just ask the genie for a time machine, then go back about five minutes and try again.

Jefferson Lab: Speedmath - Inequalities
It’s more about quality than quantity, but how quickly can you speed through inequality problems? Try this game and then see if you can beat your own time! Or, play a friend and engage in some healthy competition. Just don’t let it turn ugly.