3.7 Absolute Value Equations and Inequalities

3.7 Absolute Value Equations and Inequalities I can solve equations and inequalities involving absolute value.

What are the solutions of |x| + 2 = 9 • Solve using inverse operations • |x| = 7 so… what is x? • x = 7 or x = -7 • Why? Solving an Absolute Value Equation

What about |2x – 5| = 13? • To solve an equation in the form |A| = b, where A represents a variable expression, solve both A = b and A = -b. • 2x – 5 =13 and 2x – 5 = -13 • x = 9 or x = -4 Key Concept

Since the absolute value is the distance between a number and zero, an absolute value cannot be negative. • Solve 3|2z + 9| + 12 = 10 • Subtract 12: 3|2z + 9| = -2 • Divide by 3: |2z + 9| = - • Absolute value cannot be negative so there is no solution Absolute Value Equations

Absolute value inequalities can be written as compound inequalities. • |n – 1| < 2 can be written • -2 < n – 1 < 2 • Add 1 to each part: -1 < n < 3 Compound Inequalities

Solve and graph |n – 2| > 7 • -7 > n – 2 > 7 • -5 > n > 9 You try!

Application

ODDS ONLY • P. 211 #17-21,33-39, 47-59 Assignment

3.7 Absolute Value Equations and Inequalities