Downloaded 567 times
![The solution set of an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. To indicate that an endpoint is included in the solution set, a bracket, [ or ], is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4 interval notation](https://image.slidesharecdn.com/solving-inequalities-algebra-24180/75/Solving-Inequalities-Algebra-2-64-2048.jpg)
![The solution set of an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. To indicate that an endpoint is included in the solution set, a bracket, [ or ], is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4 interval notation -7](https://image.slidesharecdn.com/solving-inequalities-algebra-24180/75/Solving-Inequalities-Algebra-2-65-2048.jpg)
![The solution set of an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. To indicate that an endpoint is included in the solution set, a bracket, [ or ], is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4 interval notation -7 interval notation](https://image.slidesharecdn.com/solving-inequalities-algebra-24180/75/Solving-Inequalities-Algebra-2-66-2048.jpg)
Uploaded byrfant
Solving Inequalities (Algebra 2)
The document discusses various methods for solving inequalities, including: - Properties for adding, subtracting, multiplying, and dividing terms within an inequality - Using set-builder and interval notation to describe the solution set of an inequality - Graphical representations using open and closed circles to indicate whether a number is or isn't part of the solution set The document provides examples of applying these different techniques to solve specific inequalities.
In this document
Powered by AI
Introduction to solving inequalities, including vocabulary like set-builder and interval notation. Trichotomy property explained.
Discusses addition and subtraction properties of inequalities, emphasizing the addition and subtraction rules and their effects on inequality.
Covers multiplication and division properties of inequalities, with specific attention to the reversal of inequality signs when multiplying or dividing by negative numbers.
Describes solution sets of inequalities using set-builder notation with examples involving numbers like 4 and -7.
Explains solution sets in interval notation, detailing inclusion and exclusion of endpoints with brackets and parentheses.
Wrap-up of the lesson on inequalities, presenting credits and references.
More Related Content
Similar to Solving Inequalities (Algebra 2)
Solving Inequalities (Algebra 2)
- 1.
- 2. Solving Inequalities Vocabulary 1) set-builder notation 2) interval notation Solve inequalities.
- 3. For any tworeal numbers, a and b , exactly one of the following statements is true . Solving Inequalities
- 4. For any tworeal numbers, a and b , exactly one of the following statements is true . Solving Inequalities
- 5. For any tworeal numbers, a and b , exactly one of the following statements is true . Solving Inequalities
- 6. For any tworeal numbers, a and b , exactly one of the following statements is true . Solving Inequalities
- 7. For any tworeal numbers, a and b , exactly one of the following statements is true . This is known as the Trichotomy Property Solving Inequalities
- 8. For any tworeal numbers, a and b , exactly one of the following statements is true . This is known as the Trichotomy Property or the property of order . Solving Inequalities
- 9. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Solving Inequalities
- 10. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Addition Property of Inequality For any real numbers a , b , and c : Solving Inequalities
- 11. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Addition Property of Inequality For any real numbers a , b , and c : Solving Inequalities a b
- 12. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Addition Property of Inequality For any real numbers a , b , and c : Solving Inequalities a b a+c b+c c
- 13. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Addition Property of Inequality For any real numbers a , b , and c : Solving Inequalities a b a+c b+c c
- 14. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Addition Property of Inequality For any real numbers a , b , and c : Solving Inequalities a b a+c b+c
- 15. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Addition Property of Inequality For any real numbers a , b , and c : Solving Inequalities a b a+c b+c
- 16. Adding the samenumber to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality. Addition Property of Inequality For any real numbers a , b , and c : Solving Inequalities a b a+c b+c
- 17. Subtraction Propertyof Inequality For any real numbers a , b , and c : Solving Inequalities
- 18. Subtraction Propertyof Inequality For any real numbers a , b , and c : Solving Inequalities a b
- 19. Subtraction Propertyof Inequality For any real numbers a , b , and c : Solving Inequalities a-c b-c a b c
- 20. Subtraction Propertyof Inequality For any real numbers a , b , and c : Solving Inequalities a-c b-c a b c
- 21. Subtraction Propertyof Inequality For any real numbers a , b , and c : Solving Inequalities a-c b-c a b
- 22. Subtraction Propertyof Inequality For any real numbers a , b , and c : Solving Inequalities a-c b-c a b
- 23. Subtraction Propertyof Inequality For any real numbers a , b , and c : Solving Inequalities a-c b-c a b
- 24.
- 25.
- 26. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. a
- 27. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. a a
- 28. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. a a
- 29. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. We use a closed circle (dot) to indicate that a IS part of the solution set. a a
- 30.
- 31.
- 32. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. a
- 33. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. a a
- 34. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. a a
- 35. Solving Inequalities We use an open circle (dot) to indicate that a is NOT part of the solution set. We use a closed circle (dot) to indicate that a IS part of the solution set. a a
- 36. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Solving Inequalities
- 37. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities
- 38. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Multiplication Property of Inequality For any real numbers a , b , and c : However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities
- 39. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Multiplication Property of Inequality For any real numbers a , b , and c : However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities c is positive:
- 40. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Multiplication Property of Inequality For any real numbers a , b , and c : However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities c is positive:
- 41. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Multiplication Property of Inequality For any real numbers a , b , and c : However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities c is positive:
- 42. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Multiplication Property of Inequality For any real numbers a , b , and c : However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities c is positive: c is negative:
- 43. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Multiplication Property of Inequality For any real numbers a , b , and c : However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities c is positive: c is negative:
- 44. Multiplying or dividingeach side of an inequality by a positive number does not change the truth of the inequality. Multiplication Property of Inequality For any real numbers a , b , and c : However , multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed . Solving Inequalities c is positive: c is negative:
- 45. Division Propertyof Inequality Most books run us through the “rules” for division. Why is this not necessary? Solving Inequalities
- 46. Division Propertyof Inequality Most books run us through the “rules” for division. Why is this not necessary? Solving Inequalities HINT: is the same as
- 47. Division Propertyof Inequality Most books run us through the “rules” for division. Why is this not necessary? Solving Inequalities HINT: is the same as
- 48. Division Propertyof Inequality Most books run us through the “rules” for division. Why is this not necessary? So, see rules for multiplication! Solving Inequalities HINT: is the same as
- 49. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities 4
- 50. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities 4 set-builder notation
- 51. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities Read: { x “such that” x is less than 4 } 4 set-builder notation
- 52. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities Read: { x “such that” x is less than 4 } 4 set-builder notation Identify the variable used
- 53. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities Read: { x “such that” x is less than 4 } 4 set-builder notation Identify the variable used Describe the limitations or boundary of the variable
- 54. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities -7
- 55. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities -7 set-builder notation
- 56. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities Read: { x “such that” x is greater than or equal to negative 7 } -7 set-builder notation
- 57. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities Read: { x “such that” x is greater than or equal to negative 7 } Identify the variable used -7 set-builder notation
- 58. The solution setof an inequality can also be described by using set-builder notation . Solving Inequalities Read: { x “such that” x is greater than or equal to negative 7 } Identify the variable used Describe the limitations or boundary of the variable -7 set-builder notation
- 59. The solution setof an inequality can also be described by using interval notation . Solving Inequalities
- 60. The solution setof an inequality can also be described by using interval notation . Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively.
- 61. The solution setof an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively.
- 62. The solution setof an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4
- 63. The solution setof an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4 interval notation
- 64. The solution setof an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. To indicate that an endpoint is included in the solution set, a bracket, [ or ], is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4 interval notation
- 65. The solution setof an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. To indicate that an endpoint is included in the solution set, a bracket, [ or ], is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4 interval notation -7
- 66. The solution setof an inequality can also be described by using interval notation . To indicate that an endpoint is not included in the solution set, a parenthesis, ( or ), is used. To indicate that an endpoint is included in the solution set, a bracket, [ or ], is used. Solving Inequalities The infinity symbols and are used to indicate that a set is unbounded in the positive or negative direction, respectively. 4 interval notation -7 interval notation
- 67. End of Lesson Solving Inequalities
- 68. Credits PowerPointcreated by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant http://robertfant.com