(AND INEQUALITIES…) ABSOLUTE VALUE EQUATIONS. Case 1 Case 2 The quantity within the absolute value symbols is positive. |x| = 6 x = 6 The quantity within.

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Presentation transcript:

(AND INEQUALITIES…) ABSOLUTE VALUE EQUATIONS

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…

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

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**

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

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

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! TRY SOME ANSWERS!!!

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

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