1. Copyright © 2011 Pearson Education, Inc. Equations Involving Absolute Value 8.2 1.Solve equations involving absolute value.

2. | 3 | = | 0 | = | 2.5 | = | – 7 | = | – 4.8 | = 3 7 4.8 0 2.5 True or False? The absolute value of a number is always positive. False The absolute value of a number is either positive or 0. The absolute value of a number is non-negative. Absolute Value > 0 ≥ 0 Non-negative

3. | x | = 5 Absolute Value Equations x = 5 x = – 5 SameOpposite | x | = –2 No Solution Two Solutions Absolute Value Property If |x| = a, where x is a variable or an expression and a  0, then x = a or x =  a.

4. SolvingAbsolute Value Equations Solving Absolute Value Equations 1. Isolate the absolute value so that the equation is in the form |ax + b| = c.  If c < 0, the equation has no solution. 2. Separate the absolute value into two equations, ax + b = c and ax + b =  c. 3. Solve both equations.

5. Absolute Value Equations Same Opposite Drop the absolute value bars! Keep the absolute value bars! 1. Isolate 2. Two Cases 3. Solve

6. Absolute Value Equations Same Opposite Drop the absolute value bars! Keep the absolute value bars! 1. Isolate 2. Two Cases 3. Solve

7. Absolute Value Equations 1. Isolate 2. Two Cases 3. Solve No Solution

8. Absolute Value Equations Same Opposite 1. Isolate 2. Two Cases 3. Solve

9. Opposite Absolute Value Equations with 2 Absolute Values | 5 | = | 5 | Same Opposite | –8 | = | –8 | | 5 | = | –5 | | –8 | = | 8 | Two cases!

10. Absolute Value Equations with 2 Absolute Values Same Opposite

11. Absolute Value Equations with 2 Absolute Values Same Opposite

12. Absolute Value Equations with 2 Absolute Values Same Opposite No Solution