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# Absolute Value Equations (Algebra 2)

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Students review the definition of absolute value, and the empty set. Students practice solving absolute value equations.

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### Absolute Value Equations (Algebra 2)

1. 1. Solving Absolute Value Equations
2. 2. You'll Learn To: Vocabulary 1) absolute value 2) empty set <ul><li>Evaluate expressions involving absolute values. </li></ul><ul><li>Solve absolute value equations. </li></ul>Solving Absolute Value Equations
3. 3. Solving Absolute Value Equations Seismologists use the Richter scale to express the Magnitudes of earthquakes. This scale ranges from 1 to 10, 10 being the highest.
4. 4. Solving Absolute Value Equations Seismologists use the Richter scale to express the Magnitudes of earthquakes. This scale ranges from 1 to 10, 10 being the highest. The uncertainty in the estimate of a magnitude E is about Plus or minus 0.3 unit.
5. 5. Solving Absolute Value Equations Seismologists use the Richter scale to express the Magnitudes of earthquakes. This scale ranges from 1 to 10, 10 being the highest. The uncertainty in the estimate of a magnitude E is about Plus or minus 0.3 unit. This means that an earthquake with a magnitude estimated at 6.1 might actually have a magnitude as low as 5.8 or as high as 6.4.
6. 6. Solving Absolute Value Equations Seismologists use the Richter scale to express the Magnitudes of earthquakes. This scale ranges from 1 to 10, 10 being the highest. The uncertainty in the estimate of a magnitude E is about Plus or minus 0.3 unit. This means that an earthquake with a magnitude estimated at 6.1 might actually have a magnitude as low as 5.8 or as high as 6.4. These extremes can be described by the absolute value equation
7. 7. Solving Absolute Value Equations Seismologists use the Richter scale to express the Magnitudes of earthquakes. This scale ranges from 1 to 10, 10 being the highest. The uncertainty in the estimate of a magnitude E is about Plus or minus 0.3 unit. This means that an earthquake with a magnitude estimated at 6.1 might actually have a magnitude as low as 5.8 or as high as 6.4. Richter Scale 0 10 E These extremes can be described by the absolute value equation
8. 8. The absolute value of a number is its distance from zero on the number line. Solving Absolute Value Equations
9. 9. The absolute value of a number is its distance from zero on the number line. Since distance is nonnegative (positive), the absolute value of a number is always nonnegative. Solving Absolute Value Equations
10. 10. The absolute value of a number is its distance from zero on the number line. Since distance is nonnegative (positive), the absolute value of a number is always nonnegative. The symbol is used to represent the absolute value of a number x . Solving Absolute Value Equations
11. 11. Absolute Value For any real number a , if a is positive or zero, the absolute value of a is a. Solving Absolute Value Equations
12. 12. Absolute Value For any real number a , if a is positive or zero, the absolute value of a is a. 0 a Solving Absolute Value Equations distance from zero = a
13. 13. Absolute Value For any real number a , if a is positive or zero, the absolute value of a is a. 0 a For any real number a , if a is negative, the absolute value of a is a. -a Solving Absolute Value Equations distance from zero = a distance from zero = a
14. 14. Absolute Value For any real number a , if a is positive or zero, the absolute value of a is a. 0 a For any real number a , if a is negative, the absolute value of a is a. -a For any real number a, Solving Absolute Value Equations distance from zero = a distance from zero = a
15. 15. Absolute Value For any real number a , if a is positive or zero, the absolute value of a is a. 0 a For any real number a , if a is negative, the absolute value of a is a. -a For any real number a, and Solving Absolute Value Equations distance from zero = a distance from zero = a
16. 16. Solving Absolute Value Equations
17. 17. Solving Absolute Value Equations
18. 18. Solving Absolute Value Equations
19. 19. Solving Absolute Value Equations
20. 20. Solving Absolute Value Equations
21. 21. Solving Absolute Value Equations
22. 22. Solving Absolute Value Equations
23. 23. Solving Absolute Value Equations negative side:
24. 24. Solving Absolute Value Equations negative side: positive side:
25. 25. Solving Absolute Value Equations negative side: positive side:
26. 26. Solving Absolute Value Equations negative side: positive side:
27. 27. Solving Absolute Value Equations negative side: positive side: Solution set is: { 8, 42 }
28. 28. Solving Absolute Value Equations
29. 29. Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
30. 30. Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
31. 31. Solving Absolute Value Equations negative side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
32. 32. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
33. 33. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
34. 34. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
35. 35. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
36. 36. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
37. 37. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
38. 38. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
39. 39. Solving Absolute Value Equations negative side: positive side: Step 1) Isolate the absolute value expression by dividing both sides of the equation by 3 .
40. 40. Solving Absolute Value Equations
41. 41. Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12 .
42. 42. Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12 .
43. 43. Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12 . Absolute values are all NONNEGATIVE !
44. 44. Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12 . Absolute values are all NONNEGATIVE !
45. 45. Solving Absolute Value Equations Step 1) Isolate the absolute value expression by dividing both sides of the equation by – 12 . Absolute values are all NONNEGATIVE ! This is referred to as an EMPTY SET .
46. 46. Basic Absolute Value Absolute Value EquationOffset from Zero End of Lesson Solving Absolute Value Equations
47. 47. Credits PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant http://robertfant.com