9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

Sections 6.5­ 6.6      Absolute Value Equations and Inequalities

Steps:1.  Treat the absolute value as you would a variable and isolate it!  First by using + or - and then by using * or division.  2.  Once the absolute value is on the left ALONE, you will rewrite the problem into 2 equations.  3.  Write exactly what you see the first time and the second time the right side becomes a negative.4.  Solve each of the equations separately.5.  Graph the 2 ANSWERS as dots on a number line...no shading.

Examples:1. 2.

3.

9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

4.5.

6.  7. 8. 

Absolute Value InequalitiesSteps:1-2.  Same as absolute value equations.3.  Write exactly what you see the first time and the second time the inequality FLIPS and the right side becomes negative.4.  Solve each inequality separately.5.  If the ORIGINAL problems reads LESS THAN or LESS THAN OR EQUAL TO you will shade between the two numbers that you get.  IF the original problem reads GREATER THAN or GREATER THAN OR EQUAL TO then shade opposite ends of the graph.  

GO LA

9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

GO  LA!!!   Greater than is OR             Less than is AND                    (shade on ENDS)                 (shade between)

9. 

10.

9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

11.  12. 

13.  14. 

15.  Negatives with Absolute Values:

    = to a negative means NO SOLUTION < or < to a negative means NO SOLUTION > or > to a negaive means ALL REAL #s

9.20 Absolute Value Equations and Inequalities Notes

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September 20, 2013

Compound Inequalities:

16. 17.

18.