Chapter 2

Playing with Real Numbers

In This Chapter

Working with equations and inequalities

Mastering radicals and exponents

If you’re taking a pre-calculus class, you’ve already taken Algebra I and II and survived (whew!). You may also be thinking, “I’m sure glad that’s over; now I can move on to some new stuff.” Although pre-calculus presents many new and wonderful ideas and techniques, these new ideas build on the solid-rock foundation of algebra. Alas, we must refresh your memory a bit and test just how sturdy your foundation is.

We assume that you have certain algebra skills down cold, but we begin this book by reviewing some of the tougher ones that become the fundamentals of pre-calculus. In this chapter, we review solving inequalities, absolute-value equations and inequalities, and radicals and rational exponents. We also introduce a new way to express solution sets: interval notation.

Solving Inequalities

By now you’re familiar with equations and how to solve them. Pre-calculus teachers generally assume that you know how to solve equations, so most courses begin with inequalities. An inequality is a mathematical sentence indicating that two expressions aren’t equal. The following symbols express inequalities:

Less than: <

Less than or equal to: ≤

Greater than: >

Greater ...

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