This work extends naturally to absolute value
inequalities. Again, there is no need to create
two inequalities when using the transformational
approach. Take a simple example: |x – 3| > 4. This
is read as, “The distance from x to 3 is greater than
4.” Visually, it is modeled as shown in figure 4.
From the representation, students can determine
that the solution is x > 7 or x < –1. When the inequality
symbol is the is-less-than symbol, the problem
becomes finding points whose distance is less than
a given value from the anchor point. Students readily
catch on to this approach as an extension to their
understanding of absolute value equations. The
appendix (p. 597) provides practice with this idea.
Encourage students to check their solutions by substituting
values within each of the graph’s intervals,
a technique they will use later when they learn to
examine critical points of a function in calculus