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1.3 – Solving Equations. The Language of Mathematics.

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1 1.3 – Solving Equations

2 The Language of Mathematics

3 1.3 – Solving Equations The Language of Mathematics Example 1

4 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression.

5 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten.

6 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten.

7 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 7

8 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 7

9 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. + 7

10 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. + 7

11 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 10x + 7

12 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 10x + 7 (b) The product of the cube of a number and negative six.

13 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 10x + 7 (b) The product of the cube of a number and negative six.

14 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 10x + 7 (b) The product of the cube of a number and negative six. x 3

15 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 10x + 7 (b) The product of the cube of a number and negative six. x 3

16 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 10x + 7 (b) The product of the cube of a number and negative six. -6x 3

17 1.3 – Solving Equations The Language of Mathematics Example 1 Write an algebraic expression for each verbal expression. (a) Seven more than the product of a number and ten. 10x + 7 (b) The product of the cube of a number and negative six. -6x 3

18 Write a verbal expression for each equation. (c) 2n + 3 = -1

19 Write a verbal expression for each equation. (c) 2n + 3 = -1

20 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number

21 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number

22 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and

23 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and

24 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three

25 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three

26 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is

27 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is

28 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one.

29 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4

30 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4

31 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number

32 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number

33 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is

34 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is

35 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is the same number

36 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is the same number

37 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is the same number

38 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is the same number and

39 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is the same number and

40 Write a verbal expression for each equation. (c) 2n + 3 = -1 Two times a number and three is negative one. (d) 3a = a + 4 Three times a number is the same number and four.

41 Properties of Equality

42 PropertiesExamples

43 Properties of Equality Properties Reflexive Examples

44 Properties of Equality Properties Reflexive Examples -7 + n = -7 + n

45 Properties of Equality Properties Reflexive Symmetric Examples -7 + n = -7 + n

46 Properties of Equality Properties Reflexive Symmetric Examples -7 + n = -7 + n 3 = 5x – 6; 5x – 6 = 3

47 Properties of Equality Properties Reflexive Symmetric Transitive Examples -7 + n = -7 + n 3 = 5x – 6; 5x – 6 = 3

48 Properties of Equality Properties Reflexive Symmetric Transitive Examples -7 + n = -7 + n 3 = 5x – 6; 5x – 6 = 3 If x=2 and 2=y, then x=y

49 Properties of Equality Properties Reflexive Symmetric Transitive Substitution Examples -7 + n = -7 + n 3 = 5x – 6; 5x – 6 = 3 If x=2 and 2=y, then x=y

50 Properties of Equality Properties Reflexive Symmetric Transitive Substitution Examples -7 + n = -7 + n 3 = 5x – 6; 5x – 6 = 3 If x=2 and 2=y, then x=y If (4+5)m = 18, then 9m=18

51 Example 2

52 Name the property illustrated by each statement.

53 Example 2 Name the property illustrated by each statement. (a) If 3m = 5n and 5n = 10p, then 3m = 10p.

54 Example 2 Name the property illustrated by each statement. (a) If 3m = 5n and 5n = 10p, then 3m = 10p. Transitive Property

55 Example 2 Name the property illustrated by each statement. (a) If 3m = 5n and 5n = 10p, then 3m = 10p. Transitive Property (b)If –11a + 2 = -3a, then –3a = -11a + 2.

56 Example 2 Name the property illustrated by each statement. (a) If 3m = 5n and 5n = 10p, then 3m = 10p. Transitive Property (b)If –11a + 2 = -3a, then –3a = -11a + 2. Symmetric Property

57 Example 3

58 Example 3 – Solving equations

59 Example 3 – Solving equations Note: REVERSE Order of Operations!

60 (a) -7(p + 8) = 21

61 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p)

62 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) +

63 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8)

64 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21

65 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p

66 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56

67 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21

68 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56

69 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p

70 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p =

71 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77

72 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7

73 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p

74 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p =

75 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11

76 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1)

77 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)

78 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+

79 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)

80 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2

81 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 =

82 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)

83 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+

84 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1)

85 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k

86 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12

87 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2

88 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 =

89 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k

90 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k +

91 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5

92 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k

93 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14

94 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5

95 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k

96 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k

97 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14

98 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 =

99 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5

100 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14

101 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k

102 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k =

103 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5

104 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5

105 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5 k

106 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5 k =

107 Example 3 – Solving equations Note: REVERSE Order of Operations! (a) -7(p + 8) = 21 -7(p) + -7(8) = 21 -7p - 56 = 21 + 56 +56 -7p = 77 -7 -7 p = -11 (b) 4(k+3)+2 = 4.5(k+1) 4(k)+4(3)+2 = 4.5(k)+4.5(1) 4k + 12 + 2 = 4.5k + 4.5 4k + 14 = 4.5k + 4.5 -4.5k -4.5k -0.5k + 14 = 4.5 - 14 - 14 -0.5k = -9.5 -0.5 -0.5 k = 19

108 Example 4

109 Solve A = ½h(a + b) for b.

110 Example 4 Solve A = ½h(a + b) for b.

111 Example 4 Solve 2·A = 2·½h(a + b) for b.

112 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b)

113 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b)

114 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = 1·h(a + b)

115 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b)

116 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h

117 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h

118 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h

119 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h 2A h

120 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h 2A = h

121 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h 2A = a + b h

122 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h 2A = a + b h -a -a

123 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h 2A = a + b h -a -a 2A h

124 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h 2A = a + b h -a -a 2A – a h

125 Example 4 Solve A = ½h(a + b) for b. 2A = 2·½h(a + b) 2A = h(a + b) h 2A = a + b h -a -a 2A – a = b h

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Identity and Equality Properties. Properties refer to rules that indicate a standard procedure or method to be followed. A proof is a demonstration of.
E QUATIONS & INEQUALITIES Properties. W HAT ARE EQUATIONS ? Equations are mathematical sentences that state two expressions are equal. Example: 2x – 5.

E QUATIONS & INEQUALITIES Properties. W HAT ARE EQUATIONS ? Equations are mathematical sentences that state two expressions are equal. Example: 2x – 5.
Mathematical Properties Algebra I. Associative Property of Addition and Multiplication The associative property means that you will get the same result.

Mathematical Properties Algebra I. Associative Property of Addition and Multiplication The associative property means that you will get the same result.
Entry Task ? LT: I can solve equations and problems by writing equations.

Entry Task ? LT: I can solve equations and problems by writing equations.
2.1 – Writing Equations. The Language of Mathematics 2.1 – Writing Equations.

2.1 – Writing Equations. The Language of Mathematics 2.1 – Writing Equations.
Algebraic proof Chapter 2 Section 6.

Algebraic proof Chapter 2 Section 6.
Chapter 1 Section 3 Solving Equations. Verbal Expressions to Algebraic Expressions Example 1: Write an algebraic expression to represent each variable.

Chapter 1 Section 3 Solving Equations. Verbal Expressions to Algebraic Expressions Example 1: Write an algebraic expression to represent each variable.
1.3 Solving Equations. A. Q,R B. Q C. N,W,Z D. All of the above Countdown 10 Response Grid.

1.3 Solving Equations. A. Q,R B. Q C. N,W,Z D. All of the above Countdown 10 Response Grid.
Reasoning with Properties from Algebra. Properties of Equality Addition (Subtraction) Property of Equality If a = b, then: a + c = b + c a – c = b – c.

Reasoning with Properties from Algebra. Properties of Equality Addition (Subtraction) Property of Equality If a = b, then: a + c = b + c a – c = b – c.
Section 2-4 Reasoning with Properties from Algebra.

Section 2-4 Reasoning with Properties from Algebra.
Section 2.4: Reasoning in Algebra

Section 2.4: Reasoning in Algebra
1. If p  q is the conditional, then its converse is ?. a. q  pb. ~q  pc. ~q  ~pd. q  ~p 2. Which statement is always true? a. x = xb. x = 2c. x =

1. If p  q is the conditional, then its converse is ?. a. q  pb. ~q  pc. ~q  ~pd. q  ~p 2. Which statement is always true? a. x = xb. x = 2c. x =
Chapter 2 Section 4 Reasoning in Algebra. Properties of Equality Addition Property of Equality If, then. Example: ADD 5 to both sides! Subtraction Property.

Chapter 2 Section 4 Reasoning in Algebra. Properties of Equality Addition Property of Equality If, then. Example: ADD 5 to both sides! Subtraction Property.
Algebraic Proofs.

Algebraic Proofs.

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