1.6 Absolute Value Equations and Inequalities

Solving an Absolute Value Equation• What is the solution of | 2x – 1 | = 5? Graph the

solution.

| 2x – 1 | = 5

2x – 1 = 5 OR 2x – 1 = -5

2x = 6 2x = -4

x = 3 OR x = -2

Solving a Multi-Step Absolute Value Equation

• What is the solution of 3| x + 2 | - 1 = 8? Graph the solution.

3| x + 2 | - 1 = 8

3 | x + 2 | = 9

| x + 2 | = 3

x + 2 = 3 OR x + 2 = -3

x = 1 x = -5

Checking for Extraneous Solutions• What is the solution of | 3x + 2 | = 4x + 5? Graph

the solution.

| 3x + 2 | = 4x + 5 3x + 2 = 4x + 5 OR 3x + 2 = -(4x + 5) 3x = 4x + 3 3x + 2 = -4x - 5

-x = 3 7x = -7 x = -3 x = -1

• Since x = -3 does not satisfy the original equation, -3 is an extraneous solution. The only solution to the equation is x = -1.

Solving the Absolute Value Inequality | A | < b

• What is the solution of | 2x – 1 | < 5? Graph the solution.

| 2x – 1 | < 5

-5 < 2x – 1 < 5

-4 < 2x < 6

-2 < x < 3

Solving the Absolute Value Inequality | A | ≥ b

• What is the solution of | 2x + 4 | ≥ 6? Graph the solution.

| 2x + 4 | ≥ 6

2x + 4 ≤ -6 OR 2x + 4 ≥ 6

2x ≤ -10 2x ≥ 2

x ≤ -5 OR x ≥ 1

More Practice!!!!!

• Homework – Textbook p. 46 #10 – 36.