1. Linear Equations in One Variable

2. Basic Ideas and Definitions
An equation is a sentence that expresses the equality of two algebraic expressions.

3. Basic Ideas and Definitions
An equation is a sentence that expresses the equality of two algebraic expressions.
Consider the equation
2x+1=7

4. Basic Ideas and Definitions
An equation is a sentence that expresses the equality of two algebraic expressions.
Consider the equation
2x+1=7
We say 2(3) +1=7 is true.

5. Basic Ideas and Definitions
An equation is a sentence that expresses the equality of two algebraic expressions.
Consider the equation
2x+1=7
We say 2(3) +1=7 is true.
We say that 3 satisfies the equation.

6. Basic Ideas and Definitions
Algebraic Expressions
8x + 9
y - 4

7. Basic Ideas and Definitions
A Linear Equation in one variable involves only real numbers and one variable raised to the first power
x + 1 = -2
x - 3 = 5
2k + 5 = 10

8. Basic Ideas and Definitions
A Linear Equation in one variable can be written in the form
Ax + B = C

9. Basic Ideas and Definitions
Any number that satisfies the equation is called a solution or root to the equation.

10. Solution Set
The set of all solutions to
an equation is called the solution set to the equation.

11. Determine whether each equation is satisfied by the number following
Example 1
Determine whether each equation
is satisfied by the number following
the equation

12. Determine whether each equation is satisfied by the number following
Example 1
Determine whether each equation
is satisfied by the number following
the equation

13. Determine whether each equation is satisfied by the number following
Example 1
Determine whether each equation
is satisfied by the number following
the equation

14. Determine whether each equation is satisfied by the number following
Example 1
Determine whether each equation
is satisfied by the number following
the equation

15. Determine whether each equation is satisfied by the number following
Example 1
Determine whether each equation
is satisfied by the number following
the equation

16. Determine whether each equation is satisfied by the number following
Example 1
Determine whether each equation
is satisfied by the number following
the equation

17. Solving Equations
To solve an equation means to find its solution set.
The most basic method for solving equations involves the properties of equality.

18. Properties of Equality
Addition-Subtraction Property of Equality
The same real number may be added to or subtracted from each side of an equation without changing the solution set.

19. Properties of Equality
Multiplication-Division Property of Equality
Each side of an equation may be multiplied by or divided by he same real number without changing the solution set.

20. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

21. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

22. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

23. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

24. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

25. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

26. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

27. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

28. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

29. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

30. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

31. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

32. Solve the equation 4x - 2x - 5 = 4 + 6x + 3
Example 1
Solve the equation 4x - 2x - 5 = 4 + 6x + 3

33. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

34. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

35. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

36. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

37. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

38. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

39. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

40. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

41. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

42. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

43. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

44. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

45. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

46. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

47. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

48. Solve the Equation 2(k - 5) + 3k = k + 6
Example 2
Solve the Equation 2(k - 5) + 3k = k + 6

49. Example 3 Solve the Equation

50. Example 3 Solve the Equation

51. Example 3 Solve the Equation

52. Example 3 Solve the Equation

53. Example 3 Solve the Equation

54. Example 3 Solve the Equation

55. Example 3 Solve the Equation

56. Example 3 Solve the Equation

57. Example 3 Solve the Equation

58. Example 3 Solve the Equation

59. Example 3 Solve the Equation

60. Example 3 Solve the Equation

61. Example 3 Solve the Equation

62. Example 3 Solve the Equation

63. Example 3 Solve the Equation

64. Example 3 Solve the Equation

65. Example 3 Solve the Equation

66. Example 3 Solve the Equation

67. Example 3 Solve the Equation

68. Example 3 Solve the Equation

69. .06x + .09(15-x)=.07(15)
Example 4 Solve

70. .06x + .09(15-x)=.07(15)
Example 4 Solve

71. .06x + .09(15-x)=.07(15)
Example 4 Solve

72. .06x + .09(15-x)=.07(15)
Example 4 Solve

73. .06x + .09(15-x)=.07(15)
Example 4 Solve

74. .06x + .09(15-x)=.07(15)
Example 4 Solve

75. .06x + .09(15-x)=.07(15)
Example 4 Solve

76. .06x + .09(15-x)=.07(15)
Example 4 Solve

77. .06x + .09(15-x)=.07(15)
Example 4 Solve

78. .06x + .09(15-x)=.07(15)
Example 4 Solve

79. .06x + .09(15-x)=.07(15)
Example 4 Solve

80. .06x + .09(15-x)=.07(15)
Example 4 Solve

81. .06x + .09(15-x)=.07(15)
Example 4 Solve

82. .06x + .09(15-x)=.07(15)
Example 4 Solve

83. .06x + .09(15-x)=.07(15)
Example 4 Solve

84. .06x + .09(15-x)=.07(15)
Example 4 Solve

85. .06x + .09(15-x)=.07(15)
Example 4 Solve

86. .06x + .09(15-x)=.07(15)
Example 4 Solve

87. .06x + .09(15-x)=.07(15)
Example 4 Solve

88. .06x + .09(15-x)=.07(15)
Example 4 Solve

89. .06x + .09(15-x)=.07(15)
Example 4 Solve

90. .06x + .09(15-x)=.07(15)
Example 4 Solve

91. .06x + .09(15-x)=.07(15)
Example 4 Solve

92. Example 5 Solve
5x-9 = 4(x-3)

93. Example 5 Solve
5x-9 = 4(x-3)

94. Example 5 Solve
5x-9 = 4(x-3)

95. Example 5 Solve
5x-9 = 4(x-3)

96. Example 5 Solve
5x-9 = 4(x-3)

97. Example 5 Solve
5x-9 = 4(x-3)

98. Example 5 Solve
5x-9 = 4(x-3)

99. Example 5 Solve
5x-9 = 4(x-3)

100. Example 5
Solve 5x - 15 = 5(x-3)

101. Example 5
Solve 5x - 15 = 5(x-3)

102. Example 5
Solve 5x - 15 = 5(x-3)

103. Example 5
Solve 5x - 15 = 5(x-3)

104. Example 5
Solve 5x - 15 = 5(x-3)

105. Example 5
Solve 5x - 15 = 5(x-3)

106. Example 5
Solve 5x - 15 = 5(x-3)

107. Example 5
Solve 5x - 15 = 5(x-3)

108. Example 5
Solve 5x - 15 = 5(x-3)

109. Example 5
Solve 5x - 15 = 5(x-4)

110. Example 5
Solve 5x - 15 = 5(x-4)

111. Example 5
Solve 5x - 15 = 5(x-4)

112. Example 5
Solve 5x - 15 = 5(x-4)

113. Example 5
Solve 5x - 15 = 5(x-4)

114. Example 5
Solve 5x - 15 = 5(x-4)

115. Example 5
Solve 5x - 15 = 5(x-4)
Contradiction

116. Example 5
Solve 5x - 15 = 5(x-4)
Contradiction

117. Identity, Conditional Equation, Contradiction
An identity is an equation that is satisfied by every number for which both sides are defined.

118. Identity, Conditional Equation, Contradiction
A conditional equation is an equation that is satisfied by at least one number but is not an identity.

119. Identity, Conditional Equation, Contradiction
A Contradiction is an equation whose solution is the empty set.

120. L 1.1 #
Every Other Odd Problem
1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, etc.