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.
