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Integrated Math 2 Section 3-7
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- 2. Essential Questions How doyou solve and graph inequalities on a number line? How do you solve problems involving inequalities? Where you’ll see this: Communications, health, fitness, hobbies, safety, business
- 3. Vocabulary 1. Solve anInequality: 2. Addition Property of Inequality:
- 4. Vocabulary 1. Solve anInequality: Find all values that make the inequality true 2. Addition Property of Inequality:
- 5. Vocabulary 1. Solve anInequality: Find all values that make the inequality true 2. Addition Property of Inequality:
- 6. Vocabulary 1. Solve anInequality: Find all values that make the inequality true 2. Addition Property of Inequality: If a < b, then a + c < b + c
- 7. Vocabulary 1. Solve anInequality: Find all values that make the inequality true 2. Addition Property of Inequality: If a < b, then a + c < b + c If a > b, then a + c > b + c
- 8. Vocabulary 1. Solve anInequality: Find all values that make the inequality true 2. Addition Property of Inequality: If a < b, then a + c < b + c If a > b, then a + c > b + c If you add to one side of an inequality, you add to the other
- 9. Vocabulary 3. Multiplication andDivision Properties of Inequality:
- 10. Vocabulary 3. Multiplication andDivision Properties of Inequality: If a < b and c > 0, then ac < bc
- 11. Vocabulary 3. Multiplication andDivision Properties of Inequality: If a < b and c > 0, then ac < bc If a > b and c > 0, then ac > bc
- 12. Vocabulary 3. Multiplication andDivision Properties of Inequality: If a < b and c > 0, then ac < bc If a > b and c > 0, then ac > bc If a < b and c < 0, then ac > bc
- 13. Vocabulary 3. Multiplication andDivision Properties of Inequality: If a < b and c > 0, then ac < bc If a > b and c > 0, then ac > bc If a < b and c < 0, then ac > bc If a > b and c < 0, then ac < bc
- 14. Vocabulary 3. Multiplication andDivision Properties of Inequality: If a < b and c > 0, then ac < bc If a > b and c > 0, then ac > bc If a < b and c < 0, then ac > bc If a > b and c < 0, then ac < bc This is the same for division!
- 15. Vocabulary 3. Multiplication andDivision Properties of Inequality: If a < b and c > 0, then ac < bc If a > b and c > 0, then ac > bc If a < b and c < 0, then ac > bc If a > b and c < 0, then ac < bc This is the same for division! This means that if we multiply or divide by a negative, we have to flip the sign.
- 16. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22
- 17. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7
- 18. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 −n ≤ −2
- 19. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 −n ≤ −2 −1 −1
- 20. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 −n ≤ −2 −1 −1 n≥2
- 21. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 −n ≤ −2 −1 −1 n≥2 -3 -2 -1 0 1 2 3 4 5
- 22. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 −n ≤ −2 −1 −1 n≥2 -3 -2 -1 0 1 2 3 4 5
- 23. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 −n ≤ −2 −1 −1 n≥2 -3 -2 -1 0 1 2 3 4 5
- 24. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 +4 +4 −n ≤ −2 −1 −1 n≥2 -3 -2 -1 0 1 2 3 4 5
- 25. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 +4 +4 −n ≤ −2 13x > 26 −1 −1 n≥2 -3 -2 -1 0 1 2 3 4 5
- 26. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 +4 +4 −n ≤ −2 13x > 26 −1 −1 13 13 n≥2 -3 -2 -1 0 1 2 3 4 5
- 27. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 +4 +4 −n ≤ −2 13x > 26 −1 −1 13 13 n≥2 x >2 -3 -2 -1 0 1 2 3 4 5
- 28. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 +4 +4 −n ≤ −2 13x > 26 −1 −1 13 13 n≥2 x >2 -3 -2 -1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5
- 29. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 +4 +4 −n ≤ −2 13x > 26 −1 −1 13 13 n≥2 x >2 -3 -2 -1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5
- 30. Example 1 Solve and graph each inequality. a. 7 − n ≤ 5 b. 13x − 4 > 22 −7 −7 +4 +4 −n ≤ −2 13x > 26 −1 −1 13 13 n≥2 x >2 -3 -2 -1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5
- 31. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8
- 32. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4
- 33. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 x ≤ −4
- 34. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 x ≤ −4 -7 -6 -5 -4 -3 -2 -1 0 1
- 35. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 x ≤ −4 -7 -6 -5 -4 -3 -2 -1 0 1
- 36. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 x ≤ −4 -7 -6 -5 -4 -3 -2 -1 0 1
- 37. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 −3 −3 x ≤ −4 -7 -6 -5 -4 -3 -2 -1 0 1
- 38. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 −3 −3 −2x ≤ 5 x ≤ −4 -7 -6 -5 -4 -3 -2 -1 0 1
- 39. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 −3 −3 −2x ≤ 5 x ≤ −4 −2 −2 -7 -6 -5 -4 -3 -2 -1 0 1
- 40. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 −3 −3 −2x ≤ 5 x ≤ −4 −2 −2 5 x≥− 2 -7 -6 -5 -4 -3 -2 -1 0 1
- 41. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 −3 −3 −2x ≤ 5 x ≤ −4 −2 −2 5 x≥− 2 -7 -6 -5 -4 -3 -2 -1 0 1 -3 -2 -1 0 1
- 42. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 −3 −3 −2x ≤ 5 x ≤ −4 −2 −2 5 x≥− 2 -7 -6 -5 -4 -3 -2 -1 0 1 -3 -2 -1 0 1
- 43. Example 1 Solve and graph each inequality. c. − 4x ≥ 16 d. − 2x + 3 ≤ 8 −4 −4 −3 −3 −2x ≤ 5 x ≤ −4 −2 −2 5 x≥− 2 -7 -6 -5 -4 -3 -2 -1 0 1 -3 -2 -1 0 1
- 44. When multiplying/dividing bya negative:
- 45. When multiplying/dividing bya negative: You are multiplying by the opposite, so use the opposite sign.
- 46. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80?
- 47. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles
- 48. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles 39 + .42m
- 49. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles 39 + .42m ≤ 80
- 50. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles 39 + .42m ≤ 80 −39 −39
- 51. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles 39 + .42m ≤ 80 −39 −39 .42m ≤ 41
- 52. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles 39 + .42m ≤ 80 −39 −39 .42m ≤ 41 .42 .42
- 53. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles 39 + .42m ≤ 80 −39 −39 13 .42m ≤ 41 m ≤ 97 .42 .42 21
- 54. Example 2 Matt Mitarnowski’sRentals charges $39 per day, plus $.42 per mile driven. If Fuzzy Jeff rents a car for one day, what possible distances can he drive and keep his total rental charge to a maximum of $80? m = # miles 39 + .42m ≤ 80 −39 −39 13 .42m ≤ 41 m ≤ 97 .42 .42 21 Jeff can drive up to 97 miles.
- 55.
- 56. Homework p. 134 #1-11 all, 13-45 odd “Behold the turtle. He makes progress only when he sticks his neck out.” - James Bryant Conant