1. Solving Absolute Value Equations Goals: Solve equations involving absolute values Rewrite absolute value inequalities in compound form and solve

2. Definition The absolute value of a number, x, is the distance the number is from 0. Since distance is nonnegative, the absolute value of a number is always nonnegative. x , if x is positive

3. Definition The absolute value of a number, x, is the distance the number is from 0. Since distance is nonnegative, the absolute value of a number is always nonnegative. x , if x is positive 0 , if x is 0

4. Definition The absolute value of a number, x, is the distance the number is from 0. Since distance is nonnegative, the absolute value of a number is always nonnegative. x , if x is positive 0 , if x is 0 -x , if x is negative

5. If you take the negative of an absolute value, Then your answer becomes negative. !!!CAUTION!!!

6. , then the x can be equal If the to either 6 or -6. Therefore, when taking the absolute value of an equation, there are TWO possible solutions: OR Absolute Value Equations

7. Now solve both equations separately: Write your solutions together: x = -7 or 3 Absolute Value Equations

8. EXAMPLES: 1) 2) 3) 4)

9. EXAMPLES: 1) 2) 3) 4) x = -2 or 8

10. EXAMPLES: 1) 2) 3) 4) x = -2 or 8 x = -6 or 1

11. EXAMPLES: 1) 2) 3) 4) x = -2 or 8 x = -6 or 1 x = -10 or -6

12. EXAMPLES: 1) 2) 3) 4) x = -2 or 8 x = -6 or 1 x = -10 or -6 -11 2 x = -4 or

13. The way to solve multi-step absolute value equations is like solving a multi-step linear equation. Instead of solving by isolating the variable by undoing 1st: addition/subtraction 2nd: multiplication/division You isolate the absolute value by undoing 1st: addition/subtraction outside the abs. value 2nd: multiplication/division outside the abs. value Multi-Step Absolute Value Equations

14. Walk-Through: Solve the following -7 3 x = 3 or

15. x = -12 or -2 Walk-Through: Solve the following

16. Solve the following absolute value equations: 1) 2) 3) Try the Following On Your Own:

17. Solve the following: 1) x = or 4 2) 3) -2 3 Solutions:

18. Solve the following: 1) x = or 4 2) x = or 3) -2 3 -9 2 19 2 Solutions:

19. Solve the following: 1) x = or 4 2) x = -1 or 6 3) x = -6 or 0 -2 3 Solutions: