1.8 Absolute Value Equations and Inequalities

Miller & Gerken, College Algebra 2e — Pages 180-189

Learning Objectives

For \(|u| = a\) where \(a \geq 0\):

\[u = a \quad \text{or} \quad u = -a\]

For \(|u| < a\) where \(a > 0\):

\[-a < u < a\]

(This is an AND compound inequality)

For \(|u| > a\) where \(a > 0\):

\[u < -a \quad \text{or} \quad u > a\]

(This is an OR compound inequality)

Think of \(|u| < a\) as "distance from 0 is less than \(a\)" (near zero).

Think of \(|u| > a\) as "distance from 0 is greater than \(a\)" (far from zero).

Example 1. Example 1 (p. XX)

Work through textbook example…

Problem 1 (p. XX, #YY)

Problem:

My Work:

Answer:

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