Possibility 2: k < 0. Case 1: (The boundary equation |M| = k) If M is an algebraic expression and k is negative, then the solution set for |M| = k is the null set. The absolute value cannot be negative! Example: The solution |–2x – 6| = –3 is the null set because the

# Author: DrDel

# Law of Trichotomy Applied to Absolute Value Inequalities in One Variable Part I

For the sake of simplicity, the following discussion of absolute value equations and inequalities will be restricted to absolute values of linear expressions. Much of this essay is true more generally, but this current discussion is explicitly for Intermediate and College Algebra classes. Extensions can easily be made in other courses when necessary. Recall that