1. (AND INEQUALITIES…) ABSOLUTE VALUE EQUATIONS

2. Case 1 Case 2 The quantity within the absolute value symbols is positive. |x| = 6 x = 6 The quantity within the absolute value symbols is negative. |x| = 6 x = -6 To solve an absolute value equation, you must consider two cases…

3. Case 1 The quantity within the absolute value symbols is positive 3x + 4 = 16- 4 3x = 12 ÷3 x = 4 The quantity within the absolute value symbols is negative 3x + 4 = -16 - 4 3x = -20 ÷3 ÷3 x = -20/3 Example 1: |3x + 4| = 16 CHECK to see if both of these are actually solutions!

4. Example 2…Example 3 |x| - 3 = 6 +3 |x| = 9 x = 9, x = -9 **TWO ANSWERS** 2|x + 1| = 12 ÷2 |x + 1| = 6 x + 1 = 6x + 1 = -6 x = 5, x = -7 **TWO ANSWERS**

5. PAUSE… TRY THESE 1.|x+3| + 1 = 10 2.|3x – 1| = 53 3.|2x + 2| - 3 = 17 4.3|x – 9| = 27

6. Case 1 Case 2 Set up as it is shown, < 3 x + 4< 3 - 4 - 4 x < -1 Set up for other possible answers > -3 x + 4 > -3 - 4 - 4 x > -7 INEQUALITIES!!! |x + 4| < 3

7. Case 1 Case 2 x < -1 x > -7 INEQUALITIES!!! |x + 4| < 3 Is this an “AND” or an “OR” compound inequality?? (Try writing it together… Does it work?) The final answer is -7 < x < -1 it is an “AND” compound inequality… GRAPH! -8-7-6-5-4-3-2-1 TRY SOME ANSWERS!!!

8. Case 1 Case 2 2x – 1 > 9 +1 +1 2x > 10 x > 5 2x – 1 < -9 +1 +1 2x < -8 x < -4 |2x – 1| > 9 What would your Cases be? PLUG IN SOME SAMPLE ANSWERS AND SEE IF IT MAKES SENSE… WHITE BOARD!!

9. WORKBOOK PG. 43 # 1-9 TRY TO GRAPH ALSO!! STOP… Classwork/HOMEWORK!!