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Algebra 2 Interactive Chalkboard
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2. Splash Screen

3. Lesson 1-1 Expressions and Formulas
Lesson 1-2 Properties of Real Numbers
Lesson 1-3 Solving Equations
Lesson 1-4 Solving Absolute Value Equations
Lesson 1-5 Solving Inequalities
Lesson 1-6 Solving Compound and Absolute Value Inequalities
Contents

4. Example 1 Simplify an Expression Example 2 Evaluate an Expression
Example 3 Expression Containing a Fraction Bar
Example 4 Use a Formula
Lesson 1 Contents

5. Find the value of First, subtract 2 from 7. Then cube 5.
Multiply 125 by 3.
Subtract 375 from 384.
Finally, divide 9 by 3.
Answer: The value is 3.
Example 1-1a

6. Find the value of
Answer: 9
Example 1-1b

7. Replace s with 2 and t with 3.4.
Evaluate if and
Replace s with 2 and t with 3.4.
Find 22.
Subtract 3.4 from 4.
Multiply 3.4 and 0.6.
Subtract 2.04 from 2.
Answer: The value is –0.04.
Example 1-2a

8. Evaluate if and
Answer: –110
Example 1-2b

9. Evaluate the numerator and the denominator separately.
Evaluate if , , and
Evaluate the numerator and the denominator separately.
Multiply 40 by –2.
Example 1-3a

10. Simplify the numerator and the denominator. Then divide.
Answer: The value is –9.
Example 1-3b

11. Evaluate if and
Answer: –23
Example 1-3c

12. Replace h with 8, b1 with 13, and b2 with 25.
Find the area of a trapezoid with base lengths of 13 meters and 25 meters and a height of 8 meters.
Area of a trapezoid
Replace h with 8, b1 with 13, and b2 with 25.
Add 13 and 25.
Multiply 8 by .
Multiply 4 and 38.
Answer: The area of the trapezoid is square meters.
Example 1-4a

13. The formula for the volume V of a pyramid is ,
where B represents the area of the base and h is
the height of the pyramid. Find the volume of the
pyramid shown below.
Answer: 50 cm3
Example 1-4b

14. End of Lesson 1

15. Example 1 Classify Numbers
Example 2 Identify Properties of Real Numbers
Example 3 Additive and Multiplicative Inverses
Example 4 Use the Distributive Property to Solve a Problem
Example 5 Simplify an Expression
Lesson 2 Contents

16. Name the sets of numbers to which belongs.
Answer: rationals (Q) and reals (R)
Example 2-1a

17. Name the sets of numbers to which belongs.
The bar over the 9 indicates that those digits repeat forever.
Answer: rationals (Q) and reals (R)
Example 2-1b

18. Name the sets of numbers to which belongs.
lies between 2 and 3 so it is not a whole number.
Answer: irrationals (I) and reals (R)
Example 2-1c

19. Name the sets of numbers to which belongs.
Answer: naturals (N), wholes (W), integers (Z), rationals (Q) and reals (R)
Example 2-1d

20. Name the sets of numbers to which –23.3 belongs.
Answer: rationals (Q) and reals (R)
Example 2-1e

21. Name the sets of numbers to which each number belongs. a.d. e
Answer: rationals (Q) and reals (R)
Answer: rationals (Q) and reals (R)
Answer: irrationals (I) and reals (R)
Answer: naturals (N), wholes (W), integers (Z) rationals (Q) and reals (R)
Answer: rationals (Q) and reals (R)
Example 2-1f

22. Name the property illustrated by .
The Additive Inverse Property says that a number plus its opposite is 0.
Answer: Additive Inverse Property
Example 2-2a

23. Name the property illustrated by .
The Distributive Property says that you multiply each term within the parentheses by the first number.
Answer: Distributive Property
Example 2-2b

24. Name the property illustrated by each equation. a.
Answer: Identity Property of Addition
Answer: Inverse Property of Multiplication
Example 2-2c

25. Identify the additive inverse and multiplicative inverse for –7.
Since –7 + 7 = 0, the additive inverse is 7.
Since the multiplicative inverse is
Answer: The additive inverse is 7, and the multiplicative
inverse is
Example 2-3a

26. Identify the additive inverse and multiplicative inverse for .
Since the additive inverse is
Since the multiplicative inverse is
Answer: The additive inverse is and the multiplicative inverse is 3.
Example 2-3b

27. Answer: additive: –5; multiplicative:
Identify the additive inverse and multiplicative inverse for each number.
a. 5 b.
Answer: additive: –5; multiplicative:
Answer: additive: multiplicative:
Example 2-3c

28. There are two ways to find the total amount spent on stamps.
Postage Audrey went to a post office and bought eight 34-cent stamps and eight 21-cent postcard stamps. How much did Audrey spend altogether on stamps?
There are two ways to find the total amount spent on stamps.
Method 1
Multiply the price of each type of stamp by 8 and then add.
Example 2-4a

29. Answer: Audrey spent a total of $4.40 on stamps.
Method 2
Add the prices of both types of stamps and then multiply the total by 8.
Answer: Audrey spent a total of $4.40 on stamps.
Notice that both methods result in the same answer.
Example 2-4b

30. Chocolate Joel went to the grocery store and bought 3 plain chocolate candy bars for $0.69 each and 3 chocolate-peanut butter candy bars for $0.79 each. How much did Joel spend altogether on candy bars?
Answer: $4.44
Example 2-4c

31. Distributive Property
Simplify
Distributive Property
Multiply.
Commutative Property (+)
Distributive Property
Answer:
Simplify.
Example 2-5a

32. Simplify .
Answer:
Example 2-5b

33. End of Lesson 2

34. Example 1 Verbal to Algebraic Expression
Example 2 Algebraic to Verbal Sentence
Example 3 Identify Properties of Equality
Example 4 Solve One-Step Equations
Example 5 Solve a Multi-Step Equation
Example 6 Solve for a Variable
Example 7 Apply Properties of Equality
Example 8 Write an Equation
Lesson 3 Contents

35. Write an algebraic expression to represent 3 more than a number.
Answer:
Example 3-1a

36. Write an algebraic expression to represent 6 times the cube of a number.
Answer:
Example 3-1b

37. Write an algebraic expression to represent the square of a number decreased by the product of 5 and the same number.
Answer:
Example 3-1c

38. Write an algebraic expression to represent twice the difference of a number and 6.
Answer:
Example 3-1d

39. Write an algebraic expression to represent each verbal expression.
a. 6 more than a number
b. 2 less than the cube of a number
c. 10 decreased by the product of a number and 2
d. 3 times the difference of a number and 7
Answer:
Answer:
Answer:
Answer:
Example 3-1e

40. Write a verbal sentence to represent .
Answer: The sum of 14 and 9 is 23.
Example 3-2a

41. Write a verbal sentence to represent .
Answer: Six is equal to –5 plus a number.
Example 3-2b

42. Write a verbal sentence to represent .
Answer: Seven times a number minus 2 is 19.
Example 3-2c

43. Write a verbal sentence to represent each equation. a.
Answer: The difference between 10 and 3 is 7.
Answer: Five is equal to the sum of 2 and a number.
Answer: Three times a number plus 2 equals 11.
Example 3-2d

44. Answer: Substitution Property of Equality
Name the property illustrated by the statement if xy = 28 and x = 7, then 7y = 28.
Answer: Substitution Property of Equality
Example 3-3a

45. Name the property illustrated by the statement .
Answer: Reflexive Property of Equality
Example 3-3b

46. Name the property illustrated by each statement. a.
Answer: Symmetric Property of Equality
Answer: Transitive Property of Equality
Example 3-3c

47. Solve . Check your solution.
Original equation
Add 5.48 to each side.
Simplify.
Check:
Original equation
Substitute 5.5 for s.
Simplify.
Answer: The solution is 5.5.
Example 3-4a

48. Solve . Check your solution.
Original equation
Multiply each side by the
multiplicative inverse of
Simplify.
Example 3-4b

49. Answer: The solution is 36.
Check:
Original equation
Substitute 36 for t.
Simplify.
Answer: The solution is 36.
Example 3-4c

50. Solve each equation. Check your solution. a.b.
Answer: –2
Answer: 15
Example 3-4d

51. Distributive and Substitution Properties
Solve
Original equation
Distributive and Substitution Properties
Commutative, Distributive, and Substitution Properties
Addition and Substitution Properties
Division and Substitution Properties
Answer: The solution is –19.
Example 3-5a

52. Solve
Answer: –6
Example 3-5b

53. Geometry The area of a trapezoid is
where A is the area, b1 is the length of one base, b2
is the length of the other base, and h is the height of
the trapezoid. Solve the formula for h.
Example 3-6a

54. Area of a trapezoid Multiply each side by 2. Simplify.
Divide each side by .
Simplify.
Example 3-6b

55. Answer:
Example 3-6c

56. Geometry The perimeter of a rectangle is where P is the perimeter,
Geometry The perimeter of a rectangle is where P is the perimeter, is the length, and w is the width of the rectangle. Solve the formula for w. w
Answer:
Example 3-6d

57. Multiple-Choice Test Item what is the value of A B
C D
Example 3-7a

58. Read the Test Item
You are asked to find the value of the expression 4g – 2. Your first thought might be to find the value of g and then evaluate the expression using this value. However, you are not required to find the value of g. Instead, you can use the Subtraction Property of Equality on the given equation to find the value of 4g – 2.
Example 3-7b

59. Subtract 7 from each side.
Solve the Test Item
Original equation
Subtract 7 from each side.
Answer: B
Example 3-7c

60. Multiple-Choice Test Item what is the value of A 12 B 6
C –6 D –12
Answer: D
Example 3-7d

61. the cost for a carpenter
Home Improvement Carl wants to replace the 5 windows in the 2nd-story bedrooms of his home. His neighbor Will is a carpenter and he has agreed to help install them for $250. If Carl has budgeted $1000 for the total cost, what is the maximum amount he can spend on each window?
Explore Let c represent the cost of each window.
Plan
The number of windows
times
the cost per window
plus
the cost for a carpenter
equals
the total cost. 5 c +
250 =
1000
Example 3-8a

62. Subtract 250 from each side.
Solve
Original equation
Subtract 250 from each side.
Simplify.
Divide each side by 5.
Simplify.
Answer: Carl can afford to spend $150 on each window.
Example 3-8b

63. Examine. The total cost to replace five windows at $150
Examine The total cost to replace five windows at $150 each is 5(150) or $750. Add the $250 cost of the carpenter to that, and the total bill to replace the windows is or $ Thus, the answer is correct.
Example 3-8c

64. Home Improvement Kelly wants to repair the siding on her house
Home Improvement Kelly wants to repair the siding on her house. Her contractor will charge her $300 plus $150 per square foot of siding. How much siding can she repair for $1500?
Answer: 8 ft2
Example 3-8d

65. End of Lesson 3

66. Example 1 Evaluate an Expression with Absolute Value
Example 2 Solve an Absolute Value Equation
Example 3 No Solution
Example 4 One Solution
Lesson 4 Contents

67. Evaluate Replace x with 4. Simplify –2(4) first. Subtract 8 from 6.
Add.
Answer: The value is 4.7.
Example 4-1a

68. Evaluate
Answer: –13.7
Example 4-1b

69. Solve Check your solutions.
Case 1 or
Case 2
Check:
Answer: The solutions are 5 or –11. Thus, the solution set is
Example 4-2a

70. Solve Check your solutions.
Answer:
Example 4-2b

71. Subtract 5 from each side.
Solve
Original equation
Subtract 5 from each side.
This sentence is never true.
Answer: The solution set is .
Example 4-3a

72. Solve
Answer: 
Example 4-3b

73. Solve Check your solutions.
Case 1 or
Case 2
There appear to be two solutions, 11 or
Example 4-4a

74. Answer: Since , the only solution is 11. The solution set is {11}.
Check:
Answer: Since , the only solution is 11.
The solution set is {11}.
Example 4-4b

75. Solve
Answer: {6}
Example 4-4c

76. End of Lesson 4

77. Example 1 Solve an Inequality Using Addition or Subtraction
Example 2 Solve an Inequality Using Multiplication or Division
Example 3 Solve a Multi-Step Inequality
Example 4 Write an Inequality
Lesson 5 Contents

78. Solve Graph the solution set on a number line.
Original inequality
Subtract 4y from each side.
Simplify.
Subtract 2 from each side.
Simplify.
Rewrite with y first.
Example 5-1a

79. A circle means that this point is not included in the solution set.
Answer: Any real number greater than –5 is a solution of this inequality.
A circle means that this point is not included in the solution set.
Example 5-1b

80. Solve Graph the solution set on a number line.
Answer:
Example 5-1c

81. –40  p p  –40 Solve Graph the solution set on a number line.
Original inequality
Divide each side by –0.3, reversing the inequality symbol.
–40  p
Simplify.
p  –40
Rewrite with p first.
Example 5-2a

82. Answer: The solution set is
A dot means that this point is included in the solution set.
Example 5-2b

83. Solve Graph the solution set on a number line.
Answer:
Example 5-2c

84. Solve Graph the solution set on a number line.
Original inequality
Multiply each side by 2.
Add –x to each side.
Divide each side by –3, reversing the inequality symbol.
Example 5-3a

85. Answer: The solution set is and is graphed below.
Example 5-3b

86. Solve Graph the solution set on a number line.
Answer:
Example 5-3c

87. Explore Let the number of gallons of gasoline that Alida buys.
Consumer Costs Alida has at most $10.50 to spend at a convenience store. She buys a bag of potato chips and a can of soda for $1.55. If gasoline at this store costs $1.35 per gallon, how many gallons of gasoline can Alida buy for her car, to the nearest tenth of a gallon?
Explore Let the number of gallons of gasoline that Alida buys.
Plan The total cost of the gasoline is 1.35g. The cost of the chips and soda plus the total cost of the gasoline must be less than or equal to $ Write an inequality.
Example 5-4a

88. $10.50. The cost of chips & soda plus the cost of gasoline
is less than or equal to
$10.50.
1.55 +
1.35g 
10.50
Solve
Original inequality
Subtract from each side.
Simplify.
Divide each side by 1.35.
Simplify.
Example 5-4b

89. Answer: Alida can buy up to 6.6 gallons of gasoline for her car.
Examine Since is actually greater than 6.6, Alida will have enough money if she gets no more than 6.6 gallons of gasoline.
Example 5-4c

90. Rental Costs Jeb wants to rent a car for his vacation
Rental Costs Jeb wants to rent a car for his vacation. Value Cars rents cars for $25 per day plus $0.25 per mile. How far can he drive for one day if he wants to spend no more that $200 on car rental?
Answer: up to 700 miles
Example 5-4d

91. End of Lesson 5

92. Example 1 Solve an “and” Compound Inequality
Example 2 Solve an “or” Compound Inequality
Example 3 Solve an Absolute Value Inequality (<)
Example 4 Solve an Absolute Value Inequality (>)
Example 5 Solve a Multi-Step Absolute Value Inequality
Example 6 Write an Absolute Value Inequality
Lesson 6 Contents

93. Solve Graph the solution set on a number line.
Method 1 Write the compound inequality using the word and. Then solve each inequality.
and
Method 2 Solve both parts at the same time by adding 2 to each part. Then divide each part by 3.
Example 6-1a

94. Graph the solution set for each inequality and find their intersection.
Example 6-1b

95. Solve Graph the solution set on a number line.
Answer:
Example 6-1c

96. Solve or Graph the solution set on a number line.
Solve each inequality separately. or
Answer: The solution set is
Example 6-2a

97. Solve Graph the solution set on a number line.
Answer:
Example 6-2b

98. Solve Graph the solution set on a number line.
You can interpret to mean that the distance between d and 0 on a number line is less than 3 units. To make true, you must substitute numbers for d that are fewer than 3 units from 0.
Notice that the graph of is the same as the graph of d > –3 and d < 3.
All of the numbers between –3 and 3 are less than 3 units from 0.
Answer: The solution set is
Example 6-3a

99. Solve Graph the solution set on a number line.
Answer:
Example 6-3b

100. Solve Graph the solution set on a number line.
You can interpret to mean that the distance between d and 0 on a number line is greater than 3 units. To make true, you must substitute values for d that are greater than 3 units from 0.
Notice that the graph of is the same as the graph of
All of the numbers not between –3 and 3 are greater than 3 units from 0.
Answer: The solution set is
Example 6-4a

101. Solve Graph the solution set on a number line.
Answer:
Example 6-4b

102. Solve Graph the solution set on a number line.
is equivalent to
Solve each inequality. or
Answer: The solution set is .
Example 6-5a

103. Solve Graph the solution set on a number line.
Answer:
Example 6-5b

104. The rent for an apartment can differ from the average
Housing According to a recent survey, the average monthly rent for a one-bedroom apartment in one city is $750. However, the actual rent for any given one-bedroom apartment might vary as much as $250 from the average.
Write an absolute value inequality to describe this situation.
Let the actual monthly rent.
The rent for an apartment can differ from the average
by as much as
$250. 
250
Answer:
Example 6-6a

105. –r –r r Solve the inequality to find the range of monthly rent.
Rewrite the absolute value inequality as a compound inequality. Then solve for r. –r –r r
Answer: The solution set is The actual rent falls between $500 and $1000, inclusive.
Example 6-6b

106. a. Write an absolute value inequality to describe this situation.
Health The average birth weight of a newborn baby is 7 pounds. However, this weight can vary by as much as 4.5 pounds.
a. Write an absolute value inequality to describe this situation.
b. Solve the inequality to find the range of birth weights for newborn babies.
Answer:
Answer: The birth weight of a newborn baby will fall between 2.5 pounds and 11.5 pounds, inclusive.
Example 6-6c

107. End of Lesson 6

108. Explore online information about the information introduced in this chapter.
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Algebra2.com

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