Compound Inequalities (Algebra 2)

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Students learn of Compound Inequalities and Absolute Value Inequalities.

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Compound Inequalities (Algebra 2)

  1. 1. Solving Compound and Absolute Value Inequalities
  2. 2. Solving Compound and Absolute Value Inequalities Vocabulary 1) compound inequality 2) intersection 3) union <ul><li>Solve compound inequalities. </li></ul><ul><li>Solve absolute value inequalities. </li></ul>
  3. 3. A compound inequality consists of two inequalities joined by the word and or the word or . Solving Compound and Absolute Value Inequalities
  4. 4. A compound inequality consists of two inequalities joined by the word and or the word or . To solve a compound inequality, you must solve each part of the inequality. Solving Compound and Absolute Value Inequalities
  5. 5. A compound inequality consists of two inequalities joined by the word and or the word or . To solve a compound inequality, you must solve each part of the inequality. The graph of a compound inequality containing the word “ and ” is the intersection of the solution set of the two inequalities. Solving Compound and Absolute Value Inequalities
  6. 6. A compound inequality divides the number line into three separate regions. Solving Compound and Absolute Value Inequalities
  7. 7. A compound inequality divides the number line into three separate regions. Solving Compound and Absolute Value Inequalities x y z
  8. 8. Solving Compound and Absolute Value Inequalities x A compound inequality divides the number line into three separate regions. The solution set will be found: in the blue (middle) region y z
  9. 9. Solving Compound and Absolute Value Inequalities x A compound inequality divides the number line into three separate regions. The solution set will be found: in the blue (middle) region y z or in the red (outer) regions.
  10. 10. A compound inequality containing the word and is true if and only if (iff), both inequalities are true. Solving Compound and Absolute Value Inequalities
  11. 11. A compound inequality containing the word and is true if and only if (iff), both inequalities are true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  12. 12. A compound inequality containing the word and is true if and only if (iff), both inequalities are true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  13. 13. A compound inequality containing the word and is true if and only if (iff), both inequalities are true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  14. 14. A compound inequality containing the word and is true if and only if (iff), both inequalities are true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  15. 15. A compound inequality containing the word or is true if one or more , of the inequalities is true. Solving Compound and Absolute Value Inequalities
  16. 16. A compound inequality containing the word or is true if one or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  17. 17. A compound inequality containing the word or is true if one or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  18. 18. A compound inequality containing the word or is true if one or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  19. 19. A compound inequality containing the word or is true if one or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalities x 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  20. 20. A compound inequality divides the number line into three separate regions. The solution set will be found: in the blue (middle) region or in the red (outer) regions. Solving Compound and Absolute Value Inequalities x y z
  21. 21. Solve an Absolute Value Inequality (<) You can interpret |a| < 4 to mean that the distance between a and 0 on a number line is less than 4 units. Solving Compound and Absolute Value Inequalities
  22. 22. Solve an Absolute Value Inequality (<) You can interpret |a| < 4 to mean that the distance between a and 0 on a number line is less than 4 units. To make |a| < 4 true, you must substitute numbers for a that are fewer than 4 units from 0. Solving Compound and Absolute Value Inequalities
  23. 23. Solve an Absolute Value Inequality (<) You can interpret |a| < 4 to mean that the distance between a and 0 on a number line is less than 4 units. To make |a| < 4 true, you must substitute numbers for a that are fewer than 4 units from 0. Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  24. 24. Solve an Absolute Value Inequality (<) You can interpret |a| < 4 to mean that the distance between a and 0 on a number line is less than 4 units. To make |a| < 4 true, you must substitute numbers for a that are fewer than 4 units from 0. Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  25. 25. Solve an Absolute Value Inequality (<) You can interpret |a| < 4 to mean that the distance between a and 0 on a number line is less than 4 units. To make |a| < 4 true, you must substitute numbers for a that are fewer than 4 units from 0. Notice that the graph of |a| < 4 is the same as the graph a > -4 and a < 4. Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  26. 26. Solve an Absolute Value Inequality (<) You can interpret |a| < 4 to mean that the distance between a and 0 on a number line is less than 4 units. To make |a| < 4 true, you must substitute numbers for a that are fewer than 4 units from 0. Notice that the graph of |a| < 4 is the same as the graph a > -4 and a < 4. All of the numbers between -4 and 4 are less than 4 units from 0. The solution set is { a | -4 < a < 4 } Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  27. 27. Solve an Absolute Value Inequality (<) You can interpret |a| < 4 to mean that the distance between a and 0 on a number line is less than 4 units. To make |a| < 4 true, you must substitute numbers for a that are fewer than 4 units from 0. Notice that the graph of |a| < 4 is the same as the graph a > -4 and a < 4. All of the numbers between -4 and 4 are less than 4 units from 0. The solution set is { a | -4 < a < 4 } Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 For all real numbers a and b , b > 0, the following statement is true: If |a| < b then, -b < a < b
  28. 28. A compound inequality divides the number line into three separate regions. The solution set will be found: in the blue (middle) region or in the red (outer) regions. Solving Compound and Absolute Value Inequalities x y z
  29. 29. Solve an Absolute Value Inequality (>) Solving Compound and Absolute Value Inequalities
  30. 30. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. Solving Compound and Absolute Value Inequalities
  31. 31. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. To make |a| > 2 true, you must substitute numbers for a that are more than 2 units from 0. Solving Compound and Absolute Value Inequalities
  32. 32. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. To make |a| > 2 true, you must substitute numbers for a that are more than 2 units from 0. Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  33. 33. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. To make |a| > 2 true, you must substitute numbers for a that are more than 2 units from 0. Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  34. 34. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. To make |a| > 2 true, you must substitute numbers for a that are more than 2 units from 0. Notice that the graph of |a| > 2 is the same as the graph a < -2 or a > 2. Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  35. 35. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. To make |a| > 2 true, you must substitute numbers for a that are more than 2 units from 0. Notice that the graph of |a| > 2 is the same as the graph a < -2 or a > 2. All of the numbers not between -2 and 2 are greater than 2 units from 0. The solution set is { a | a > 2 or a < -2 } Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3
  36. 36. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. To make |a| > 2 true, you must substitute numbers for a that are more than 2 units from 0. Notice that the graph of |a| > 2 is the same as the graph a < -2 or a > 2. All of the numbers not between -2 and 2 are greater than 2 units from 0. The solution set is { a | a > 2 or a < -2 } Solving Compound and Absolute Value Inequalities 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 For all real numbers a and b , b > 0, the following statement is true: If |a| > b then, a < -b or a > b
  37. 37. End of Lesson Solving Compound and Absolute Value Inequalities
  38. 38. Credits PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant http://robertfant.com

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