Download - Finishing from Friday
1
1
FINISHING FROM FRIDAYSolve and check for extraneous solutions
Hint: Remember the Negative| | 4 1 2 9x x
Chapter 1.6
04/21/23 04:43 2
04/21/23 04:43 2
ABSOLUTE VALUE INEQUALITIES
ABSOLUTE VALUE INEQUALITIES
Inequalities involve signs that are greater, less, and/or equal to signs.
04/21/23 04:43 3
04/21/23 04:43 3
SOLVING FOR ABSOLUTE VALUE INEQUALITIES
04/21/23 04:43 4
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 4
When Solving for Inequalities, remember:
Less ThanANDMore ThanOR
LAMO
04/21/23 04:432-8: Absolute Value Inequalities 5
5
AND VERSUS OR…When Solving for Inequalities, remember:
Less ThAND GreatOR Than
Less Than, “AND” Greater Than, “OR”
STEPS FOR SOLVING AND GRAPHING ABSOLUTE VALUE INEQUALITIES
04/21/23 04:43 6
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 6
1. Identify whether it is an AND/OR inequality (think LAMO)
2. Solve each inequality3. Check each solution and make sure
there aren’t any extraneous solutions4. Graph appropriately on number line
EXAMPLE 1Solve and graph the solution
04/21/23 04:43 7
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 7
| | 3 5x
|–8
|0
|2
AND3 5x 2x
3 5x 8x
2 and 8x x
EXAMPLE 2Solve and graph the solution
04/21/23 04:43 8
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 8
| | 4 5 13x
4 8x
|–9/2
|0
|2
2x 4 18x
9
2x
92 or
2x x
OR
YOUR TURNSolve and graph the solution
04/21/23 04:43 9
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 9
| | 2 4 3x
|–7/2
|0
|-1/2
7 1 and
2 2x x
04/21/23 04:432-8: Absolute Value Inequalities 10
EXAMPLE 3Solve and graph. 3 12 4 4 28x
04/21/23 04:432-8: Absolute Value Inequalities 11
Solve and graph. 8 4 48x
YOUR TURN
EXAMPLE 4Solve and graph the solution
04/21/23 04:43 12
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 12
| | 2 1 25x
No Solution
EXAMPLE 5Solve and graph the solution
04/21/23 04:43 13
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 13
| | 1 16x
All Real Numbers
ASSIGNMENT Finish WKST from Friday
04/21/23 04:43 14
1-6: Absolute Value Equations04/21/23 04:43 2.9: Absolute Value Inequalities 14