1

1

FINISHING FROM FRIDAYSolve and check for extraneous solutions

Hint: Remember the Negative| | 4 1 2 9x x

Chapter 1.6

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ABSOLUTE VALUE INEQUALITIES

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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1-6: Absolute Value Equations04/21/23 13:23 2.9: Absolute Value Inequalities 4

When Solving for Inequalities, remember:

Less ThanANDMore ThanOR

LAMO

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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

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1-6: Absolute Value Equations04/21/23 13:23 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

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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

EXAMPLE 2Solve and graph the solution

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1-6: Absolute Value Equations04/21/23 13:23 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

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1-6: Absolute Value Equations04/21/23 13:23 2.9: Absolute Value Inequalities 9

| | 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

EXAMPLE 4Solve and graph the solution

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1-6: Absolute Value Equations04/21/23 13:23 2.9: Absolute Value Inequalities 12

| | 2 1 25x

No Solution

EXAMPLE 5Solve and graph the solution

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1-6: Absolute Value Equations04/21/23 13:23 2.9: Absolute Value Inequalities 13

| | 1 16x

All Real Numbers

ASSIGNMENT Finish WKST from Friday

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1-6: Absolute Value Equations04/21/23 13:23 2.9: Absolute Value Inequalities 14