(AND INEQUALITIES…)

ABSOLUTE VALUE EQUATIONS

Case 1 Case 2

The quantity within the absolute value symbols is positive.

|x| = 6x = 6

The quantity within the absolute value symbols is negative.

|x| = 6x = -6

To solve an absolute value equation, you must consider two cases…

Case 1 Case 1

The quantity within the absolute value symbols is positive

3x + 4 = 16- 4 - 4

3x = 12

÷3 ÷3x = 4

The quantity within the absolute value symbols is negative

3x + 4 = -16- 4 - 4

3x = -20

÷3 ÷3x = -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 +3

|x| = 9

x = 9, x = -9 **TWO ANSWERS**

2|x + 1| = 12

÷2 ÷2

|x + 1| = 6

x + 1 = 6 x + 1 = -6

x = 5, x = -7  **TWO ANSWERS**

PAUSE… TRY THESE

1.|x+3| + 1 = 102.|3x – 1| = 533.|2x + 2| - 3 = 174.3|x – 9| = 27

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

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!!!

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!!

WORKBOOK PG. 43 # 1-9

TRY TO GRAPH ALSO!!

STOP… Classwork/HOMEWORK!!