Introduction and Summary
This chapter revisits, in more depth, a concept introduced in the Pre-Algebra SparkNote on Absolute Value .
The first section is a review of the material learned in pre-algebra. It discusses the meaning of absolute value and the notation associated with it. It then explores absolute value equations containing variables. We learn how to find a solution set to such an equation, given a replacement set.
The next section explains how to solve an absolute value equation without a specific replacement set. This is done by separating the equation into two equations without absolute value, and solving with inverse operations.
The final section explains how to solve absolute value inequalities by graphing them on a number line. It explains how to find and plot critical points and then test regions to determine which region(s) satisfy the inequality.
The concept of absolute value is tricky, because equations with absolute value generally have more than one solution. This chapter helps to alleviate the difficulties of absolute value equations and inequalities by providing concrete steps to follow when solving them. It also introduces the idea of a critical point. This idea, as well as the steps that we use, will be useful in other topics of algebra--such as graphing inequalities in more than one variable. Thus, it is important to master them now.