CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics
86
Section 1.7: Interval Notation and Linear Inequalities
Linear Inequalities
Linear Inequalities
Rules for Solving Inequalities:
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A portion of a textbook from the University of Houston Department of Mathematics, specifically from the Fundamentals of Mathematics (MATH 1300) course. It covers the topic of interval notation and linear inequalities. examples of linear inequalities, their solutions, and the conversion of these solutions to interval notation. It also includes exercises for students to practice solving linear inequalities and writing them in interval notation.
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2021/2022
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CHAPTER 1 Introductory Information and Review
86 University of Houston Department of Mathematics
Section 1.7 : Interval Notation and Linear Inequalities
Linear Inequalities
Linear Inequalities
Rules for Solving Inequalities:
SECTION 1.7 Interval Notation and Linear Inequalities
MATH 1300 Fundamentals of Mathematics 87
Interval Notation:
Example:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
MATH 1300 Fundamentals of Mathematics 89
Solution:
Additional Example 1:
Solution:
CHAPTER 1 Introductory Information and Review
90 University of Houston Department of Mathematics
Additional Example 2:
Solution:
CHAPTER 1 Introductory Information and Review
92 University of Houston Department of Mathematics
Additional Example 5:
Solution:
Additional Example 6:
Solution:
SECTION 1.7 Interval Notation and Linear Inequalities
MATH 1300 Fundamentals of Mathematics 93
Additional Example 7:
Solution:
Exercise Set 1.7: Interval Notation and Linear Inequalities
MATH 1300 Fundamentals of Mathematics 95
37. 5 x 30 38. 4 x 40 39. 2 x 5 11 40. 3 x 4 17 41. 8 3 x 20 42. 10 x 0 43. 4 x 11 7 x 4 44. 5 9 x 3 x 7 45. 10 x 7 2 x 6 46. 8 4 x 6 5 x 47. 5 8 x 4 x 1 48. x 10 8 x 9 49. 3 ( 4 5 x ) 2 ( 7 x ) 50. 4 ( 3 2 x )( x 20 ) 51. 65 31 x 21 ( x 5 ) 52. 52 x 21 31 10 x 53. 10 3 x 2 8 54. 9 2 x 3 13 55. 4 3 7 x 17 56. 19 5 4 x 3
57. 32 3 x 15 ^10 54
58. 43 5 62 x 35
Which of the following inequalities can never be true?
59. (a) 5 x 9 (b) 9 x 5 (c) 3 x 7 (d) 5 x 3 60. (a) 3 x 5 (b) 8 x 1 (c) 2 x 8 (d) 7 x 10
Answer the following.
61. You go on a business trip and rent a car for $ per week plus 23 cents per mile. Your employer will pay a maximum of $100 per week for the rental. (Assume that the car rental company rounds to the nearest mile when computing the mileage cost.)
(a) Write an inequality that models this situation. (b) What is the maximum number of miles that you can drive and still be reimbursed in full?
62. Joseph rents a catering hall to put on a dinner theatre. He pays $225 to rent the space, and pays an additional $7 per plate for each dinner served. He then sells tickets for $15 each.
(a) Joseph wants to make a profit. Write an inequality that models this situation. (b) How many tickets must he sell to make a profit?
63. A phone company has two long distance plans as follows:
Plan 1: $4.95/month plus 5 cents/minute Plan 2: $2.75/month plus 7 cents/minute
How many minutes would you need to talk each month in order for Plan 1 to be more cost- effective than Plan 2?
64. Craig’s goal in math class is to obtain a “B” for the semester. His semester average is based on four equally weighted tests. So far, he has obtained scores of 84, 89, and 90. What range of scores could he receive on the fourth exam and still obtain a “B” for the semester? (Note: The minimum cutoff for a “B” is 80 percent, and an average of 90 or above will be considered an “A”.)