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# 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:

- Translating real-world problems into symbols, and
- 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 onâ€”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 will know when we are 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.