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Compound Inequalities (Algebra 2)

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Students learn of Compound Inequalities and Absolute Value Inequalities.

Text of Compound Inequalities (Algebra 2)

  • 1. Solving Compound andAbsolute Value Inequalities

2. Solving Compound and Absolute Value InequalitiesVocabulary 1) compound inequality 2) intersection 3) union

  • Solve compound inequalities.
  • Solve absolute value inequalities.

3. Acompound inequalityconsists of two inequalities joined by the wordand or the wordor . Solving Compound and Absolute Value Inequalities 4. Acompound inequalityconsists of two inequalities joined by the wordand or the wordor . To solve a compound inequality, you must solve each part of the inequality. Solving Compound and Absolute Value Inequalities 5. Acompound inequalityconsists of two inequalities joined by the wordand or the wordor . To solve a compound inequality, you must solve each part of the inequality. The graph of a compound inequality containingthe word and is theintersectionof the solution set of the two inequalities. Solving Compound and Absolute Value Inequalities 6. Acompound inequalitydivides the number line into three separate regions. Solving Compound and Absolute Value Inequalities 7. Acompound inequalitydivides the number line into three separate regions. Solving Compound and Absolute Value Inequalitiesx y z 8. Solving Compound and Absolute Value Inequalitiesx Acompound inequalitydivides the number line into three separate regions. Thesolution setwill be found: in theblue(middle) regiony z 9. Solving Compound and Absolute Value Inequalitiesx Acompound inequalitydivides the number line into three separate regions. Thesolution setwill be found: in theblue(middle) regiony z or in thered(outer) regions. 10. A compound inequality containing the wordand is true if and only if (iff),both inequalities are true. Solving Compound and Absolute Value Inequalities 11. A compound inequality containing the wordand is true if and only if (iff),both inequalities are true. Example: Solving Compound and Absolute Value Inequalitiesx 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 12. A compound inequality containing the wordand is true if and only if (iff),both inequalities are true. Example: Solving Compound and Absolute Value Inequalitiesx 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. A compound inequality containing the wordand is true if and only if (iff),both inequalities are true. Example: Solving Compound and Absolute Value Inequalitiesx 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. A compound inequality containing the wordand is true if and only if (iff),both inequalities are true. Example: Solving Compound and Absolute Value Inequalitiesx 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 15. A compound inequality containing the wordor is true ifone or more , of the inequalities is true. Solving Compound and Absolute Value Inequalities 16. A compound inequality containing the wordor is true ifone or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalitiesx 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 17. A compound inequality containing the wordor is true ifone or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalitiesx 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. A compound inequality containing the wordor is true ifone or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalitiesx 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. A compound inequality containing the wordor is true ifone or more , of the inequalities is true. Example: Solving Compound and Absolute Value Inequalitiesx 5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 20. Acompound inequalitydivides the number line into three separate regions. Thesolution setwill be found: in theblue(middle) regionor in thered(outer) regions. Solving Compound and Absolute Value Inequalitiesx y z 21. Solve an Absolute Value Inequality( 2 to mean that the distance betweenaand0on a number line is greater than 2 units. Solving Compound and Absolute Value Inequalities 31. Solve an Absolute Value Inequality(>) You can interpret|a| > 2 to mean that the distance betweenaand0on a number line is greater than 2 units. To make|a| > 2 true, you must substitute numbers forathat are more than 2 units from0. Solving Compound and Absolute Value Inequalities 32. Solve an Absolute Value Inequality(>) You can interpret|a| > 2 to mean that the distance betweenaand0on a number line is greater than 2 units. To make|a| > 2 true, you must substitute numbers forathat are more than 2 units from0. Solving Compound and Absolute Value Inequalities5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 33. Solve an Absolute Value Inequality(>) You can interpret|a| > 2 to mean that the distance betweenaand0on a number line is greater than 2 units. To make|a| > 2 true, you must substitute numbers forathat are more than 2 units from0. Solving Compound and Absolute Value Inequalities5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 34. Solve an Absolute Value Inequality(>) You can interpret|a| > 2 to mean that the distance betweenaand0on a number line is greater than 2 units. To make|a| > 2 true, you must substitute numbers forathat are more than 2 units from0. Notice that the graph of|a| > 2is the same as the grapha < -2or a > 2. Solving Compound and Absolute Value Inequalities5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 35. Solve an Absolute Value Inequality(>) You can interpret|a| > 2 to mean that the distance betweenaand0on a number line is greater than 2 units. To make|a| > 2 true, you must substitute numbers forathat are more than 2 units from0. Notice that the graph of|a| > 2is the same as the grapha < -2or a > 2. All of the numbersnotbetween -2 and 2 are greater than 2 units from 0. The solution set is{ a | a > 2ora < -2 } Solving Compound and Absolute Value Inequalities5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 36. Solve an Absolute Value Inequality(>) You can interpret|a| > 2 to mean that the distance betweenaand0on a number line is greater than 2 units. To make|a| > 2 true, you must substitute numbers forathat are more than 2 units from0. Notice that the graph of|a| > 2is the same as the grapha < -2or a > 2. All of the numbersnotbetween -2 and 2 are greater than 2 units from 0. The solution set is{ a | a > 2ora < -2 } Solving Compound and Absolute Value Inequalities5 -4 -2 0 2 4 -5 -3 1 5 -1 -5 3 For all real numbersa andb ,b > 0,the following statement is true: If|a| > bthen,a < -bora > b 37. EndofLesson Solving Compound and Absolute Value Inequalities 38. CreditsPowerPoint created by Using Glencoes Algebra 2 text, 2005 Robert Fant http://robertfant.com

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