Solving Absolute Value Equations

1. Solving Absolute Value Equations Unit 1A Lesson 4

2. The Absolute Value Function is a famous Piecewise Function. • It has two pieces: • below zero: – x • from 0 onwards: x • x , if x> 0 • f(x) = |x| = • – x , if x < 0 f(x) =|x|

3. EXAMPLE 1 Solve | x + 2 | = 7 (x + 2) = 7     –(x + 2) = 7 x + 2 = 7       –x – 2 = 7 –9 = x x = 5             x = –9 (– 9 , 7) (5, 7)

4. EXAMPLE 2 (5, 3) (– 2 ,3)

5. Practice

6. EXAMPLE 3

7. EXAMPLE 4 We can’t get a negative value out of the absolute value. Since this isn’t possible that means there is no solution to this equation.

8. EXAMPLE 5 STEP 1 CHECK is NOT a solution!!!!

9. EXAMPLE 5 STEP 2 CHECK The only solution is

11. EXAMPLE 6 STEP 1 CHECK .

12. EXAMPLE 6 STEP 2 CHECK . Both solutions work.

14. EXAMPLE 7 STEP 1: Both inside values are EQUAL CHECK is a solution!!!!

15. STEP 2: Both inside values are EQUAL but with OPPOSITE signs Since both sides gave the same result you only have to do ONE SIDE!!!

16. CHECK is a solution!!!! Both solutions work.

18. Practice 1.

19. 2.

20. 3.

21. 4.

22. 5.