1. Splash Screen

2. 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

3. 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

4. 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

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

6. 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

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

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

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

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

11. 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

12. 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

13. Algebra II Chapter 1 Section 2

14. Drill (solve for each variable)1) 2) 3)

15. Types of Numbers
Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers

16. Real Numbers (R)
All numbers used in everyday life, the set of all rational and irrational numbers.
Ex: ½ , -3, 4.667,

17. Rational Numbers (Q)
Any number , where m and n are integers and n is a non-zero. The decimal form is either a terminating or repeating decimal.
Ex: ½ , 2.555,

18. Irrational Numbers (I)
Any number which can not be written as a fraction. The decimal form neither repeats or terminates.
Ex: …

19. Integers (Z)
All non-decimal or fractional numbers including all positive numbers, negative numbers and zero.
Ex: {...-2, -1, 0, 1, 2, 3, …}

20. Whole Numbers (W)
All Integers except for all the negative numbers.
Ex: {0, 1, 2, 3, 4, 5, ….}

21. Natural Numbers (N)
All Integers except negative numbers and zero.
Ex: {1, 2, 3, 4, 5, ….}

22. Number Chart
Real Numbers (R)
(Q)
(Z)
(w)
(N)
(I)

23. Examples -4
….. 8

24. Reciprocal
When you write a number as a fraction and switch the numerator and the denominator.
The reciprocal is the number you would multiply by to get one.

25. Real Number Properties
For any real numbers a, b, and c:
Property
Addition
Multiplication
Commutative
a + b = b + a
ab = ba
Associative
(a + b) + c = a + (b + c)
(ab)c = a(bc)
Identity
a + 0 = a
(a)(1) = a
Inverse
a + (-a) = 0
a(1/a) = 1
Distributive
a (b + c) = ab + bc

26. 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

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

28. 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

29. 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

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

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

32. 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

33. 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

34. 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

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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

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

43. Simplify .
Answer:
Example 2-5b

44. Algebra II Chapter 1 Section 3

45. DRILL Solve for x in each equation: 1) x + 13 = 20 2) x – 11 = -13

46. DRILL Solve for x in each equation: x + 13 = 20 3) 4x = 32
Divide by 4
x = x = 8
x – 11 = -13
x = - 2

47. Motivation
Math Magic
Choose a number.

48. Examples
2x + 5 = 17
2x = 12
Divide by 2 on both sides
x = 6

49. DRILL
Solve for x in each equation:
1) 2x + 13 = 27
2) 3x – 7 = -13 3)

50. Solve for x in each equation:
2x = 14
Divide both sides by 2
x = 7

51. Solve for x in each equation:
3x = -6
Divide both sides by 3
x = -2

52. Combining Like-Terms
Like terms are terms that have the exact same exponents and variables.
When you add or subtract like terms you simply add/subtract the numbers in front of the variables (coefficients) and keep the variables and exponents the same.

53. Example 4x + 7 + 3x – 2 = 33 7x + 5 = 33 - 5 - 5 7x = 28
7x = 28
Divide both sides by 7
x = 4

54. Distributive Property
When you have a number (term) in parentheses next to an expression you must multiply the number (term) out front with each part of the expression inside the parentheses.
Ex: 2(3x + 4) = 6x + 8

55. Examples 2(x + 5) = 34 2x + 10 = 34 - 10 - 10 2x = 24 x = 12
2x = 24
Divide by 2 on both sides
x = 12

56. 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

57. 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

58. 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

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

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

61. 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

62. Solve
Answer: –6
Example 3-5b

63. 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

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

65. 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

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

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

68. 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

69. 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

70. 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

71. 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