Name Class Date. Determine whether each number is a solution of the given inequality.
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1 3-1 Practice Form G Inequalities and Their Graphs Write an inequality that represents each verbal expression. 1. v is greater b is less than or equal to the product of g and 2 is less than or equal to more than k is greater than 3. Determine whether each number is a solution of the given inequality. 5. 3y + 5 < 20 a. 2 b. 0 c m 4 10 a. 1 b. 8 c x + 3 > 9 a. 0 b. 2 c. 4 3 n a. 3 b. 2 c Graph each inequality. 9. y < t z > v f 14. < c 3 3
2 3-1 Practice (continued) Form G Inequalities and Their Graphs Write an inequality for each graph Define a variable and write an inequality to model each situation. 19. The school auditorium can seat at most 1200 people. 20. For a certain swim meet, a competitor must swim faster than 23 seconds to qualify. 21. For a touch-typing test, a student must type at least 65 wpm to receive an A. Write each inequality in words. 22. n < b > x 25. z < q m 28. A local pizzeria offered a special. Two pizzas cost $ A group of students spent less than $75. They purchased three pitchers of soda for $ How many pizzas could the group purchase? 29. A student needs at least seven hours of sleep each night. The student goes to bed at 11:00 p.m. and wakes up before 6:30 a.m. Is the student getting enough sleep? Write an inequality for the number of hours of sleep the student gets each night. 4
3 3-2 Practice Form G Solving Inequalities Using Addition or Subtraction State what number you would add to or subtract from each side of the inequality to solve the inequality. 1. x 4 < 0 4. x > S m > m Solve each inequality. Graph and check your solutions. 7. y 2 < 7 8. v + 6 > c f s < n C p
4 3-2 Practice (continued) Solving Inequalities Using Addition or Subtraction Form G Solve each inequality. Justify each step. 15. y 4 + 2y > d < v p 4 + 3p > y + 2 3y m 4m + 4 > The goal of a toy drive is to donate more than 1000 toys. The toy drive already has collected 300 toys. How many more toys does the toy drive need to meet its goal? Write and solve an inequality to find the number of toys needed. 22. A family earns $1800 a month. The family s expenses are at least $1250. Write and solve an inequality to find the possible amounts the family can save each month. 23. To go to the next level in a certain video game, you must score at least 50 points. You currently have 40 points. You fall into a trap and lose 5 points. What inequality shows the points you must earn to go to the next level? 14
5 3-3 Practice Form G Solving Inequalities Using Multiplication or Division Solve each inequality. Graph and check your solution. x w > 1 < p y x k. 7. 3m > t < c 10. 3w < z > d 23
6 3-3 Practice (continued) Form G Solving Inequalities Using Multiplication or Division Solve each inequality. Graph and check your solution > 5p t 1 < n u Writing On a certain marathon course, a runner reaches a big hill that is at least 10 miles into the race. If a total marathon is 26.2 miles, how can you find the number of miles the runner still has to go? 18. You wonder if you can save money by using your cell phone for all long distance calls. Long distance calls cost $.05 per minute on your cell phone. The basic plan for your cell phone is $29.99 each month. The cost of regular phone service with unlimited long distance is $ Define a variable and write an inequality that will help you find the number of long-distance call minutes you may make and still save money. 19. The unit cost for a piece of fabric is $4.99 per yard. You have $30 to spend on material. How many feet of material could you buy? Define a variable and write an inequality to solve this problem. 24
7 3-4 Practice Form G Solving Multi-Step Inequalities Solve each inequality. Check your solutions. 1. 3f + 9 < n y p > > 60 6r j Solve each inequality. 7. 2(k + 4) 3k (4c 5) 2c > (j 3) + 3j < (2y + 3) 3y > 3(3z + 3) + 3z (d 4) + 4d x + 2 < 3x v 12 > 5v + 10 Solve each inequality, if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers w + 5 > 2(3w + 3) 16. 5r (r 2) 17. 2(6 + s) < s x < 7 + 2(x 3) 19. 2(n 3) n 20. 3(w + 3) < 9 3w 33
8 3-4 Practice (continued) Form G Solving Multi-Step Inequalities 21. A grandmother says her grandson is two years older than her granddaughter and that together, they are at least 12 years old. How old are her grandson and granddaughter? 22. A family decides to rent a boat for the day while on vacation. The boat s rental rate is $500 for the first two hours and $50 for each additional half hour. Suppose the family can spend $700 for the boat. What inequality represents the number of hours for which they can rent the boat? 23. Writing Suppose a friend is having difficulty solving 1.75(q 5) > 3(q + 2.5). Explain how to solve the inequality, showing all the necessary steps and identifying the properties you would use. 24. Open-Ended Write two different inequalities that you can solve by adding 2 to each side and then dividing each side by 12. Solve each inequality. 25. Reasoning a. Solve 3v 5 2v + 10 by gathering the variable terms on the left side and the constant terms on the right side of the inequality. b. Solve 3v 5 2v + 10 by gathering the constant terms on the left side and the variable terms on the right side of the inequality. c. Compare the results of parts (a) and (b). d. Which method do you prefer? Explain. 34
9 3-5 Practice Working With Sets Form G Write each set in roster form and in set-builder notation. 1. M is the set of integers that are greater than N is the set of even numbers that are less than P is the set of natural numbers that are factors of R is the set of odd natural numbers that are less than 12. Write each set in set-builder notation. 5. B = { 3, 2, 1, 0, 1, } 6. M = {2, 4, 6, 8, 10} 7. S = {1, 2, 3, 6, 9, 18} 8. G = {, 5, 3, 1, 1, 3, 5, } Write the solutions of each inequality in set-builder notation. 9. 2y + 5 < r + 3 > m (3x + 5) (x 7) > 10 6x 14. 2(x + 7) x 15. 3(2x + 4) + 1 > (2x 4) 1 < x 17. (x 1) x Prentice Hall Algebra 1 Teaching Resources 43
10 3-5 Practice (contined) Working With Sets Form G List all the subsets of each set. 18. {a, b, c, d} 19. {0, 3, 6, 9} 20. {car, bus, truck} 21. { 5, 5} 22. {0} 23. {red, blue, yellow} 24. Suppose U = {0, 2, 4, 6, 8, 10} is the universal set and A = {2, 4, 6}. What is A'? 25. Suppose U = {, 5, 3, 1, 3, 5, } is the universal set and R = {1, 3, 5, }. What is R'? 26. Suppose U = {x x is a multiple of 3, x 18} is the universal set and C = {21, 24, 27, 30}. What is C'? 27. Suppose U = {x x is a real number, x < 3} is the universal set and T = {x x is a real number, x < 10}. What is T'? Suppose U = {1, 2, 4, 7, 11, 15}, A = {2, 4, 7}, and B = {1, 2, 4}. Tell whether each statement is true or false. Explain your reasoning. 28. A U 29. U B 30. B A 31. B 32. Let the universal set U and set B be as defined below. What are the elements of the complement of B? Write your answer in roster form and in set-builder notation. U = {all the months in a calendar year} B = {all months that have 31 days} Prentice Hall Algebra 1 Teaching Resources 44
11 3-6 Practice Form G Compound Inequalities Write a compound inequality that represents each phrase. Graph the solutions. 1. all real numbers that are less than 3 or greater than or equal to 5 2. The time a cake must bake is between 25 minutes and 30 minutes, inclusive. Solve each compound inequality. Graph your solutions < k 2 < > y + 2 > b 1 41 or 2b m < 4 or 7m > < 2p k 3 > d or 5d c < 2 or 3c > y + 2 3(y 2) z + 3 < 7 or 2z 6 > 8 Write each interval as an inequality. Then graph the solutions. 13. ( 1, 10] 14. [ 3, 3] 15. (, 0] or (5, ) 16. [3, ) 17. (, 4) 18. [25, 50) Prentice Hall Algebra 1 Teaching Resources 53
12 3-6 Practice (continued) Form G Compound Inequalities Write each inequality or set in interval notation. Then graph the interval. 19. x < x > x < 2 or x x < 4 Write a compound inequality that each graph could represent Solve each compound inequality. Justify each step r + 2 < 5 or 7r 10 > > 0.25v > 2.5 y y or w The absorbency of a certain towel is considered normal if the towel is able to hold between six and eight ml. The first checks for materials result in absorbency measures of 6.2 ml and 7.2 ml. What possible values for the third reading m will make the average absorbency normal? 32. A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child? Prentice Hall Algebra 1 Teaching Resources 54
13 3-7 Practice Form G Absolute Value Equations and Inequalities Solve each equation. Graph and check your solutions b = = y 3 3. n + 2 = = s 3 5. x 5 = d = 49 Solve each equation. If there is no solution, write no solution. 7. r 9 = 3 8. c + 3 = = g = m d = w = v 5 = d 4 = f = 7 Solve and graph each inequality. 16. x > x < x + 3 < y + 4 > y p c 4 > t
14 3-7 Practice (continued) Form G Absolute Value Equations and Inequalities Solve each equation or inequality. If there is no solution, write no solution. 24. d + 3 = p = d + + = f = y t 1.2 = y c + 4 = < d > Write an absolute value inequality that represents each set of numbers. 33. all real numbers less than 3 units from all real numbers at most 6 units from all real numbers more than 4 units from all real numbers at least 3 units from A child takes a nap averaging three hours and gets an average of 12 hours of sleep at night. Nap time and night time sleep can each vary by 30 minutes. What are the possible time lengths for the child s nap and night time sleep? 38. In a sports poll, 53% of those surveyed believe their high school football team will win the state championship. The poll shows a margin of error of ±5 percentage points. Write and solve an absolute value inequality to find the least and the greatest percent of people that think their team will win the state championship. 64
15 3-8 Practice Form G Unions and Intersections of Sets Find each union or intersection. Let A = {1, 3, 5, 7, 9}, B = {x x is a positive odd integer less than 10}, C = {1, 2, 4, 7}, and D = {x x is a negative integer between 5 and 1}. 1. A B 2. A C 3. A D 4. B C 5. B D 6. C D 7. A B 8. A C 9. A D 10. A B C 11. D C B 12. A C D 13. A B D 14. A C D 15. B C D Draw a Venn diagram to represent the union and intersection of these sets. 16. Let V = {p, m, b, a, d, e}, W = {i, t, b, p}, and X = {g, e, r, z, p}. 17. Let L = {all negative odd integers}, M = {all negative integers greater than or equal to 5}, and N = { 3, 1, 0, 3, 1}. Prentice Hall Algebra 1 Teaching Resources 73
16 3-8 Practice (continued) Form G Unions and Intersections of Sets 18. Each student at a particular school participates in at least one type of activity sports or music. Fifty students participate in both sports and music. Two hundred students participate in sports. Fifty students participate in music only. There are a total of 250 students at the school. How many students only participate in sports? 19. A local parks department asked 300 people if they should build new basketball courts and/or new skateboard ramps. They were not allowed to answer neither. If 233 people said they want new basketball courts and 94 people said they want both new basketball courts and skateboard ramps, how many people said they wanted new skateboard ramps? Solve each inequality. Write the solutions as either the union or intersection of two sets x > 7n + 8 > w > 4d < n + 3 < t 0.75 < A salon offers three services manicures, massages, and hair styling. Five clients come in for all three services. Forty clients come in for both hair styling and manicures. Thirty-five clients come in for both manicures and massages. Fifteen clients come in for both hair styling and massages. Ten clients come in only for massages. Five clients only come in for hair styling and only two clients come in for just manicures. How many total clients are represented by the data? Prentice Hall Algebra 1 Teaching Resources 74
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