1 1 f inishing from f riday solve and check for extraneous solutions hint: remember the negative
TRANSCRIPT
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FINISHING FROM FRIDAYSolve and check for extraneous solutions
Hint: Remember the Negative| | 4 1 2 9x x
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Chapter 1.6
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ABSOLUTE VALUE INEQUALITIES
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ABSOLUTE VALUE INEQUALITIES
Inequalities involve signs that are greater, less, and/or equal to signs.
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SOLVING FOR ABSOLUTE VALUE INEQUALITIES
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When Solving for Inequalities, remember:
Less ThanANDMore ThanOR
LAMO
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AND VERSUS OR…When Solving for Inequalities, remember:
Less ThAND GreatOR Than
Less Than, “AND” Greater Than, “OR”
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STEPS FOR SOLVING AND GRAPHING ABSOLUTE VALUE INEQUALITIES
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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
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EXAMPLE 1Solve and graph the solution
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1-6: Absolute Value Equations04/21/23 13:23 2.9: Absolute Value Inequalities 7
| | 3 5x
|–8
|0
|2
AND3 5x 2x
3 5x 8x
2 and 8x x
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EXAMPLE 2Solve and graph the solution
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| | 4 5 13x
4 8x
|–9/2
|0
|2
2x 4 18x
9
2x
92 or
2x x
OR
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YOUR TURNSolve and graph the solution
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| | 2 4 3x
|–7/2
|0
|-1/2
7 1 and
2 2x x
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EXAMPLE 3Solve and graph. 3 12 4 4 28x
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Solve and graph. 8 4 48x
YOUR TURN
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EXAMPLE 4Solve and graph the solution
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| | 2 1 25x
No Solution
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EXAMPLE 5Solve and graph the solution
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| | 1 16x
All Real Numbers
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ASSIGNMENT Finish WKST from Friday
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