1. Start Here

2. Linear Inequalities in One Variable

3. Basic ideas
Statements that express the inequality of algebraic expressions are called inequalities.

4. Inequality Symbols

5. Basic ideas
We know 4 < 5 but how do we compare -4 and -5 -1 5 4 3 2 1 -5 -4 -3 -2

6. -1 5 4 3 2 1 -5 -4 -3 -2

7. -1 5 4 3 2 1 -5 -4 -3 -2

8. -1 5 4 3 2 1 -5 -4 -3 -2

9. -1 5 4 3 2 1 -5 -4 -3 -2

10. -1 5 4 3 2 1 -5 -4 -3 -2

11. -1 5 4 3 2 1 -5 -4 -3 -2

12. -1 5 4 3 2 1 -5 -4 -3 -2

13. -1 5 4 3 2 1 -5 -4 -3 -2

14. -1 5 4 3 2 1 -5 -4 -3 -2

15. -1 5 4 3 2 1 -5 -4 -3 -2

16. -1 5 4 3 2 1 -5 -4 -3 -2

17. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.

18. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true.

19. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true. -1 5 4 3 2 1 -5 -4 -3 -2

20. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true.
1.5<3 -1 5 4 3 2 1 -5 -4 -3 -2

21. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true.
1.5<3 -1 5 4 3 2 1 -5 -4 -3 -2

22. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true.
1.5<3
0<3 -1 5 4 3 2 1 -5 -4 -3 -2

23. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true.
1.5<3
0<3 -1 5 4 3 2 1 -5 -4 -3 -2

24. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true.
1.5<3
0<3
-2<3 -1 5 4 3 2 1 -5 -4 -3 -2

25. Graphing Inequalities
The statement x < 3 means that x is a real number to the left of 3 on the number line.
The numbers 1.5, 0 and -2 are all to the left of 3 on the number line so the following are true.
1.5<3
0<3
-2<3 -1 5 4 3 2 1 -5 -4 -3 -2

26. Graphing Inequalities
The set of all numbers that give a true statement when used as a replacement for x is called the solution set to the inequality. -1 5 4 3 2 1 -5 -4 -3 -2

27. Graphing Inequalities
The set of all numbers that give a true statement when used as a replacement for x is called the solution set to the inequality.
The solution set to x< 3 is all the real numbers to the left of 3 on a number line. -1 5 4 3 2 1 -5 -4 -3 -2

28. Graphing Inequalities
The set of all numbers that give a true statement when used as a replacement for x is called the solution set to the inequality.
The solution set to x< 3 is all the real numbers to the left of 3 on a number line. -1 5 4 3 2 1 -5 -4 -3 -2

29. Graphing Inequalities
The set of all numbers that give a true statement when used as a replacement for x is called the solution set to the inequality.
The solution set to x< 3 is all the real numbers to the left of 3 on a number line. -1 5 4 3 2 1 -5 -4 -3 -2

30. Open Interval

31. Open Interval (a

32. Open Interval (a

33. Open Interval (a

34. Open Interval

35. Open Interval (a )b

36. Open Interval (a )b

37. Open Interval (a )b

38. Open Interval

39. Open Interval )b

40. Open Interval )b

41. Open Interval )b

42. Half-open Interval

43. Half-open Interval [a

44. Half-open Interval [a

45. Half-open Interval [a

46. Half-opened Interval

47. Half-opened Interval (a

48. Half-opened Interval (a ]b

49. Half-opened Interval (a ]b

50. Half-opened Interval (a ]b

51. Half-opened Interval

52. Half-opened Interval [a

53. Half-opened Interval [a )b

54. Half-opened Interval [a )b

55. Half-opened Interval [a )b

56. Half-open Interval

57. Half-open Interval ]b

58. Half-open Interval ]b

59. Half-open Interval ]b

60. Closed Interval

61. Closed Interval [a

62. Closed Interval [a ]b

63. Closed Interval [a ]b

64. Closed Interval [a ]b

65. All real numbers

66. All real numbers

67. All real numbers

68. Interval Notation -1 5 4 3 2 1 -5 -4 -3 -2

69. Interval Notation -1 5 4 3 2 1 -5 -4 -3 -2

70. Interval Notation ) -1 5 4 3 2 1 -5 -4 -3 -2

71. Interval Notation ) -1 5 4 3 2 1 -5 -4 -3 -2

72. Interval Notation ) -1 5 4 3 2 1 -5 -4 -3 -2

73. Interval Notation ) -1 5 4 3 2 1 -5 -4 -3 -2

74. Interval Notation -1 5 4 3 2 1 -5 -4 -3 -2

75. Interval Notation -1 5 4 3 2 1 -5 -4 -3 -2

76. Interval Notation -1 5 4 3 2 1 -5 -4 -3 -2

77. Interval Notation [ -1 5 4 3 2 1 -5 -4 -3 -2

78. Interval Notation [ -1 5 4 3 2 1 -5 -4 -3 -2

79. Interval Notation [ -1 5 4 3 2 1 -5 -4 -3 -2

80. Interval Notation [ -1 5 4 3 2 1 -5 -4 -3 -2

81. -1 5 4 3 2 1 -5 -4 -3 -2

82. ( -1 5 4 3 2 1 -5 -4 -3 -2

83. ( -1 5 4 3 2 1 -5 -4 -3 -2

84. ( -1 5 4 3 2 1 -5 -4 -3 -2

85. ( -1 5 4 3 2 1 -5 -4 -3 -2

86. -1 5 4 3 2 1 -5 -4 -3 -2

87. ] -1 5 4 3 2 1 -5 -4 -3 -2

88. ] -1 5 4 3 2 1 -5 -4 -3 -2

89. ] -1 5 4 3 2 1 -5 -4 -3 -2

90. ] -1 5 4 3 2 1 -5 -4 -3 -2

91. A linear inequality in one variable x is any inequality of the form
Ax + b < 0 where a and b are real numbers, with

92. A linear inequality in one variable x is any inequality of the form
Ax + b < 0 where a and b are real numbers, with

93. A linear inequality in one variable x is any inequality of the form
Ax + b < 0 where a and b are real numbers, with

94. A linear inequality in one variable x is any inequality of the form
Ax + b < 0 where a and b are real numbers, with

95. A linear inequality in one variable x is any inequality of the form
Ax + b < 0 where a and b are real numbers, with

96. Properties of Inequality

97. Properties of Inequality

98. Properties of Inequality

99. Properties of Inequality

100. Properties of Inequality
Each side of an inequality may be multiplied by or divided by the same non-zero number without changing the solution set.
If the inequality is multiplied by or divided by a negative number, the inequality symbol is reversed.

101. Properties of Inequality
Each side of an inequality may be multiplied by or divided by the same non-zero number without changing the solution set.
If the inequality is multiplied by or divided by a negative number, the inequality symbol is reversed.

102. Equaivalent Inequalities
Equivalent inequalities are inequalities with the same solution set.

103. Solve x - 7 = -12

104. Solve x - 7 = -12

105. Solve x - 7 = -12

106. Solve x - 7 = -12

107. Solve x - 7 = -12

108. Solve x - 7 = -12 -1 5 4 3 2 1 -5 -4 -3 -2

109. Solve x - 7 = -12 -1 5 4 3 2 1 -5 -4 -3 -2

120. 14 18 16 10 12

121. [ 14 18 16 10 12

122. [ 14 18 16 10 12

123. [ 14 18 16 10 12

131. -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

132. ] -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

133. ] -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

134. ] -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

155. -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

156. ] -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

157. ] -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

158. ] -5 -6 -1 -2 -3 -4
-10 -9 -8 -7

189. -3 -4 2 1 -1 -2 -8 -7 -6 -5

190. ( -3 -4 2 1 -1 -2 -8 -7 -6 -5

191. ( -3 -4 2 1 -1 -2 -8 -7 -6 -5

192. ( -3 -4 2 1 -1 -2 -8 -7 -6 -5

229. -1 5 4 3 2 1 -5 -4 -3 -2

230. [ -1 5 4 3 2 1 -5 -4 -3 -2

231. [ ] -1 5 4 3 2 1 -5 -4 -3 -2

232. [ ] -1 5 4 3 2 1 -5 -4 -3 -2

233. A rental company charges $15 to rent a chain saw, plus $2 per hour.

234. A rental company charges $15 to rent a chain saw, plus $2 per hour
A rental company charges $15 to rent a chain saw, plus $2 per hour. Al Ghandi can spend no more than $35 to clear some logs from his yard.

235. A rental company charges $15 to rent a chain saw, plus $2 per hour
A rental company charges $15 to rent a chain saw, plus $2 per hour. Al Ghandi can spend no more than $35 to clear some logs from his yard. What is the maximum amount of time he can use the rented saw?

236. A rental company charges $15 to rent a chain saw, plus $2 per hour
A rental company charges $15 to rent a chain saw, plus $2 per hour. Al Ghandi can spend no more than $35 to clear some logs from his yard. What is the maximum amount of time he can use the rented saw?

246. Martha has scores of 88, 86, and 90 on here three algebra scores.

247. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class.

248. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class. What possible scores on her fourth test will earn her an A average.

249. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class. What possible scores on her fourth test will earn her an A average.

250. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class. What possible scores on her fourth test will earn her an A average.

251. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class. What possible scores on her fourth test will earn her an A average.

252. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class. What possible scores on her fourth test will earn her an A average.

253. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class. What possible scores on her fourth test will earn her an A average.

254. Martha has scores of 88, 86, and 90 on here three algebra scores
Martha has scores of 88, 86, and 90 on here three algebra scores. An average score of at least 90 will earn an A in the class. What possible scores on her fourth test will earn her an A average.

266. L 1.5 # 1- 66