Lesson 3-6 Absolute Value Equations Objectives: To solve equations and inequalities that involve absolute value.

Why should we learn this? One real-world connection is evident in manufacturing. This skill helps determine possible measurements for parts.

Definition Absolute Value The distance a number is from zero.

Examples |r| = 3 |r| > 3 |r| < 3

Absolute Value Rules To solve |A| = b, where A represents a variable expression and b>0, solve A = b or A = -b. To solve |A| > b, A > b or A < -b To solve |A| < b, -b < A < b

Steps 1. Isolate the absolute value. 2. Determine whether you need intersection (and/ “between”) or union (or) 3. Solve the compound Inequality

Example 1, page 167 a) |t| - 2 = -1 b) 3|n| = 15

You try… C) 4 = 3|w| - 2 D) Is there a solution of 2|n| = -15? Explain

Example 2, page 168 A) |c – 2| = 6b) –5.5 = |t + 2|

You try… c) |7d| = 14

Example 3, p. 169 |v – 3| > 4

You Try w + 2| > 5

Example 4 |c - 3| < 1

You Try |c – 2| < 6

SUMMARY How do I solve an absolute value equation? How do I solve an absolute value Inequality?

Summary What did you learn today?

ASSIGNMENT #3-6a, page 169, 1-71 odd and odds 81-97