Review Block 4 Vocabulary algebraic expression equivalent expressions simplify an expression coefficient evaluate solution constant inequality term equation like terms variable Lesson 4.1 ~ Expressions and Equations Write an algebraic expression for each phrase. 1. the product of nine and y 2. the sum of m and six 3. four less than the product of z and eight 4. two more than the quotient of c and five Evaluate each expression. 5. x_ 9 when x = 30 6. 6b + 5 when b = 4 2 7. 5k 7n when k = 10 and n = 2 8. 2_ 9 m + 1 _ 3 when m = 3 Determine if the number given is the solution to the equation. 9. 4x + 1 = 9 Is 2 the solution? 10. 3y 5 = 7 Is 4 the solution? 11. m 6 + 5 = 7.3 Is 15 the solution? 12. 1_ h + 2 = 0 Is 8 the solution? 4 142 Block 4 ~ Review
Lesson 4.2 ~ Solving One-Step Equations Solve each equation using an equation mat or inverse operations. Show all work necessary to justify your answer. 13. 3x = 21 14. y + 81 = 107 15. p 4 = 7 16. 3.25 = m 6.25 17. 0.2k = 1.1 18. 12 + x = _ 1 Write an algebraic equation for each sentence. Solve the equation using an equation mat or inverse operations. 19. The product of x and nine equals thirty-six. 20. The quotient of x and two is two-fifths. 21. Thirty-one less than x is negative ten. 22. The sum of x and one-half equals thirteen. 23. Kate is thinking of two numbers. The sum of the numbers is 8. If one of the numbers is 12, what is the other number? Use words and/or numbers to show how you determined your answer. 5 6 Lesson 4.3 ~ Solving Two-Step Equations 24. 8x 9 = 7 25. h + 3 = 6 26. 21 = 7 2x 4 27. 2m + 6 = 18 28. 0.5y + 1.9 = 10.4 29. 6x + 14 = 2 Write an equation for each statement. Solve the problem. Show all work necessary to justify your answer. 30. Four times a number x plus eleven is thirty-five. Find the number. 31. The number y divided by negative six decreased by seven is eleven. Find the number. 32. Partridge Middle School hosts an ice cream social each month. This month, there were eight more than three times as many people at the ice cream social than last month. There were 128 people at the ice cream social this month. How many people attended last month s ice cream social? Show all work necessary to justify your answer. Block 4 ~ Review 143
Lesson 4.4 ~ The Distributive Property Use the Distributive Property to rewrite each expression without parentheses. 33. 8(x + 10) 34. 3(5y 4) 35. 2(x 9) 36. 3(x 5) = 21 37. 8(x + 4) = 16 38. 26 = 2(3x + 1) 39. 5(0.3x + 1) = 20 40. 1_ 2 (8x + 2) = 3 41. 77 = 11(x 2) 42. Three sisters went to the movie theater together on Saturday night. It cost $7.50 for each sister to enter the theater. Each sister spent an equal amount of money at the concession stand. The evening cost the three sisters $37.50. a. Let c represent the amount of money each sister spent at the concession stand. Write an equation using the Distributive Property to represent this situation. b. How much did each sister spend at the concession stand? Show all work necessary to justify your answer. Lesson 4.5 ~ Simplifying Expressions Simplify each algebraic expression. 43. 8 7y + 6 + 10y 44. 11a + 5d a 10a 7d 45. 5(2x + 7) + x 4 46. 2(4x + 1) 7x + 2 47. 15 + 3(p + 2) 48. 13 2(x 6) 49. It takes Owen 40 minutes to get to his best friend s house. He spends m minutes riding his bike to the bus stop at a rate of 0.2 miles per minute. He gets on the bus and travels the rest of the way at a rate of 0.5 miles per minute. The total distance traveled is represented by the expression 0.2m + 0.5(40 m). a. Simplify this expression. b. Owen rides his bike for 16 minutes. How far did he ride? Use words and/or numbers to show how you determined your answer. Lesson 4.6 ~ Simplifying and Solving Equations 50. 7a + 2a 4a = 45 51. 10y + 9 3y + 1 = 59 52. 7 = 3(x + 1) + 2x 53. 2 + 1_ 5 m + 3 m + 7 = 5 54. 52 = 4(x 8) 2(x 5) 55. 40 2(d + 5) = 20 10 144 Block 4 ~ Review
Lesson 4.7 ~ Solving Equations With Variables on Both Sides 56. 4x + 35 = 11x 57. 5p 10 = 8p + 14 58. 25 9c = c 59. 0.4h + 1 = 16 1.1h 60. 3_ 8 x 2 = 1_ 8 x + 4 61. 11 + 4a = a + 5 62. An online video game rental site has a Frequent Gamers Plan. It costs $30 to join and each video game rental for members costs $2. Non-members pay a rental fee of $3.50 per rental. Let g represent the total number of video games rented. a. Write two expressions, one representing the cost for g rentals by a member and the other representing the cost of g rentals for a non-member. b. For what number of rentals would both plans cost the same amount? Use words and/or numbers to show how you determined your answer. Lesson 4.8 ~ Linear Inequalities Write an inequality for each graph shown. Use x as the variable. 63. 4 3 2 1 0 1 2 3 64. 4 3 2 1 0 1 2 3 65. 5x 20 66. x + 7 < 6 67. 10 < 3x + 1 68. x 2 < 3 69. 19 5x + 4 70. 9(x + 2) < 6x 3 71. Louis has $800 in his bank account at the beginning of the summer. He wants to have at least $500 in his account at the end of the summer. Each week he withdraws $35 for food and entertainment. a. Write an inequality for this situation. Let x represent the number of weeks he withdraws money from his account. b. How many full weeks can Louis withdraw money from his account? Tic-Tac-Toe ~ Gi v e n a n A nsw e r Write a multi-step inequality that, when solved, is represented by the given inequality. 1. x > 3 2. x < 5 3. x 4 4. x 0 5. x 1.5 6. x > 2.5 7. x 8 8. x < 10 9. x 1 _ 3 Block 4 ~ Review 145
Rachelle Adoption Agency Director CAREER FOCUS I am the director for an international adoption agency. I match orphaned children from all over the world with adoptive parents. Some adoption agencies work only with adoptions of children in the Unites States. Other agencies help families adopt children from other countries. I travel to other countries, such as India and Guatemala, to escort children to their new families. When looking at children who will be coming up for adoption, I look at their growth measurements such as how big they are, how quickly they are growing, and how tall they are. I chart a child s growth on a graph. I use math to determine what percentile they fall in for each measurement. Because I work with countries that use the metric system, I convert metric measurements to customary measurements. This helps parents in the United States better understand how healthy a child is. A person must have a degree in a related field such as social work or sociology to work on adoptions. It is also a good idea for adoption workers to get some international experience. Visiting other countries helps a person know how that culture works. This is very helpful when adopting from that country. A person just entering the field of adoptions can expect to make $26,000 - $29,000 a year. That salary varies based on how much experience the person has. Working as an adoption agent can be very difficult work. Sometimes I come across sad circumstances. However, this job is very rewarding because I can unite a child from a poor situation with a new, loving family. 146 Block 4 ~ Review