Table of contents

0. Review of Algebra(0)
1. Equations & Inequalities(0)
2. Graphs of Equations(0)
3. Functions(0)
4. Polynomial Functions(0)
5. Rational Functions(0)
6. Exponential & Logarithmic Functions(0)
7. Systems of Equations & Matrices(0)
8. Conic Sections(0)
9. Sequences, Series, & Induction(0)
10. Combinatorics & Probability(0)

1. Equations & Inequalities

Linear Inequalities

1. Equations & Inequalities

Linear Inequalities - Online Tutor, Practice Problems & Exam Prep

Linear Inequalities Practice Problems

302 problems

1PRACTICE PROBLEM

Write the equivalent interval notation for the given inequality.

x < -8

2PRACTICE PROBLEM

Write the equivalent interval notation for the given inequality.

x ≤ 4

3PRACTICE PROBLEM

Write the equivalent interval notation for the given inequality.

-5< x ≤ 9

4PRACTICE PROBLEM

Write the equivalent interval notation for the given inequality.

x ≥ 7

5PRACTICE PROBLEM

Write the equivalent interval notation for the given inequality.

x ≥ -3

6PRACTICE PROBLEM

Write the equivalent interval notation for the given inequality.

5 ≤ x

7PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. 7(x + 11) + 13 ≥ 5 + 7x

8PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. 9x - 2x + 5 < 4(x + 2)

9PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. 1 - 3x + 9(x - 3) < - 1(x - 9)

10PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. (9x + 2)/(- 5) ≤ 3x + 2

11PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. (3x - 1)/(- 4) ≤ 2 - 6x

12PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation.

13PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation.

14PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. - 3 < 6 + 9x < 42

15PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. 11 ≤ 3x + 5 ≤ 20

16PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. 6 > - 2x + 9 > - 9

17PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. - 5 ≤ (11x + 3)/6 ≤ 6

18PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. 7 ≤ (3x - 2)/4 < 13

19PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |7x - 2| < 12

20PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |7x - 2| ≥ 12

21PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |4/5 - x| ≤ 3

22PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |4/5 - x| < 3

23PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. 9|x + 2| > 81

24PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |6 - 4x| > 46

25PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |1 - 2x| > 37

26PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |1 - 2x| ≤ 37

27PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |6 - 3x| ≤ 54

28PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |(3/5)x + 3/2| ≤ 3/10

29PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |3/5 - (1/2)x| > 9/10

30PRACTICE PROBLEM

Express the solution set in interval notation for the following absolute value inequality. |0.09x + 0.9| < 0.72

31PRACTICE PROBLEM

Find the number of solutions for the given inequation.

|x + 2| = √(x+2)²

32PRACTICE PROBLEM

Solve the equation given below for x.

|3x + 7| - 4 = -3

33PRACTICE PROBLEM

Solve the equation given below for x.

|9x - 4| - 6 = -5

34PRACTICE PROBLEM

Solve the equation given below for x.

|5 - 3x| + 3 = 8

35PRACTICE PROBLEM

Solve the equation given below for x.

|6 - 6x| + 4 = 8

36PRACTICE PROBLEM

Work out the solution set of the following absolute value inequality:

|4x + 3| - 7 < 3

37PRACTICE PROBLEM

Work out the solution set of the following absolute value inequality:

|7x + 5| - 8 < 9

38PRACTICE PROBLEM

Work out the solution set of the following absolute value inequality:

|11x + 3/4| - 4 < 16

39PRACTICE PROBLEM

Work out the solution set of the following absolute value inequality:

|6x + 1/8| + 4 < 8

40PRACTICE PROBLEM

Work out the solution set of the following absolute value inequality:

|8 - 3x | + 3 ≥ 6

41PRACTICE PROBLEM

Work out the solution set of the following absolute value inequality:

|15 - 7x| + 11 ≥ 17

42PRACTICE PROBLEM

Work out the solution set of the following absolute value inequality:

|9x - 8| + 2 < -8

43PRACTICE PROBLEM

Solve the inequality given below:

|-4x + 9| - 8 < -18

44PRACTICE PROBLEM

Solve the inequality given below:

|14 - 11x| ≥ 19

45PRACTICE PROBLEM

Solve the inequality given below:

|16 - 17x| ≥ -37

46PRACTICE PROBLEM

Solve the inequality given below:

|13 - 9x| < -21

47PRACTICE PROBLEM

Solve the inequality given below:

|22 - 11x| < -23

48PRACTICE PROBLEM

Solve the equation given below for x.

|6x + 7| = 0

49PRACTICE PROBLEM

Solve the equation given below for x.

|11 + 4x| = 0

50PRACTICE PROBLEM

Solve the inequality given below:

|5.7 - 8.9x| < 0

51PRACTICE PROBLEM

Solve the inequality given below:

|2.5x - 18| < 0

52PRACTICE PROBLEM

Solve the inequality given below:

|6x + 11| > 0

53PRACTICE PROBLEM

Rewrite the following statement as an inequality.

"G is no more than 11 units from 17"

54PRACTICE PROBLEM

Rewrite the following statement as an equation utilizing absolute value and inequality symbols.

"L is no less than 5 units from 31."

55PRACTICE PROBLEM

Rewrite the following statement as an absolute-value equation. "H is no more than 29 units from 37"

56PRACTICE PROBLEM

If the temperature of a planet (in Fahrenheit) is expressed using the absolute value equation |T + 167| ≤ 41. Determine the range of temperature.

57PRACTICE PROBLEM

For x² - x to have an absolute value equal to 12, what are the two possible values that x may assume?

58PRACTICE PROBLEM

Using absolute value properties, solve the following inequality:

|4x² + 3x| = 22

59PRACTICE PROBLEM

Using absolute value properties, solve the following inequality:

|x⁴ + 6x² + 9| < 0

60PRACTICE PROBLEM

Write the solution set in interval notation for the following inequality.

7x ≥ 3(x - 6)

61PRACTICE PROBLEM

Write the solution set in interval notation for the following inequality.

-8x - 23 ≥ 2(5x - 4)

62PRACTICE PROBLEM

Write the solution set in interval notation for the following inequality.

15x - 4(x - 6) ≤ 4(4 - x)

63PRACTICE PROBLEM

Write the solution set in interval notation for the following inequality.

23 ≤ 5x -7 ≤ 33

64PRACTICE PROBLEM

Write the solution set in interval notation for the following inequality.

-12 > 7x - 4 > -18

65PRACTICE PROBLEM

Solve the following absolute-value inequality. |6 - 2a| ≥ 12

66PRACTICE PROBLEM

Solve the following absolute-value inequality. |7a - 13| > 27

67PRACTICE PROBLEM

Solve the following absolute-value inequality. |6 - 2a| - 5 > 7

68PRACTICE PROBLEM

Solve the following absolute-value inequality. |5x - 3| ≥ - 1

69PRACTICE PROBLEM

Convert the following word statement into a mathematical statement that makes use of both absolute value and inequality symbols.

"17 is at least 5 units from k."

70PRACTICE PROBLEM

Graph the solution set for the following equation:

|x| = 5

71PRACTICE PROBLEM

Graph the solution set for the following equation:

|x| = -6

72PRACTICE PROBLEM

Graph the solution set for the following inequality:

|x| > -4

73PRACTICE PROBLEM

Graph the solution set for the following inequality:

|x| > 8

74PRACTICE PROBLEM

Graph the solution set for the following inequality:

|x| < 3

75PRACTICE PROBLEM

Graph the solution set for the following inequality:

|x| ≥ 9

76PRACTICE PROBLEM

Graph the solution set for the following inequality:

|x| ≤ 6

77PRACTICE PROBLEM

Graph the solution set for the following equation:

|x| ≠ 8

78PRACTICE PROBLEM

Find the solution set for the following inequality. Express the answer in interval notation. 7x - (2x + 5) ≥ 5x - 11

79PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

4 - x/5 > 6

80PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

6(2x - 4) - 2x < 5(1 + 2x) - 10

81PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

3(x - 4) - 2(x + 6) ≥ x - 10

82PRACTICE PROBLEM

Solve the given inequality using the table shown. 2 ≤ 2x -13 < 10

83PRACTICE PROBLEM

Solve the following inequality and graph its solution set: (3x - 2)/10 ≥ 2x/5 + 1/5

84PRACTICE PROBLEM

Graph the following interval on a number line and write it in set-builder notation: (3,10]

85PRACTICE PROBLEM

Graph the following interval on a number line and write it in set-builder notation: [-8,5)

86PRACTICE PROBLEM

Graph the following interval on a number line and write it in set-builder notation: [-7,6]

87PRACTICE PROBLEM

Graph the following interval on a number line and write it in set-builder notation: (8, ∞)

88PRACTICE PROBLEM

Graph the following interval on a number line and write it in set-builder notation: [-6, ∞)

89PRACTICE PROBLEM

Graph the following interval on a number line and write it in set-builder notation: (-∞, 5)

90PRACTICE PROBLEM

Use graphs to find the intersection of the two intervals: (-5, 1) ∩ [-3, 4]

91PRACTICE PROBLEM

Use graphs to find the union of the two intervals: (-5, 1) ⋃ [-3, 4]

92PRACTICE PROBLEM

Use graphs to find the intersection of the two intervals: (-∞, 7) ∩ [1, 10)

93PRACTICE PROBLEM

Use graphs to find the union of the two intervals: (-∞, 8) ⋃ [3, 9)

94PRACTICE PROBLEM

Use graphs to find the intersection of the two intervals: [5, ∞) ∩ (9, ∞)

95PRACTICE PROBLEM

Use graphs to find the union of the two intervals: [5, ∞) ⋃ (9, ∞)

96PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

3x + 15 < 27

97PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

5x - 3 ≥ 20

98PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

-7x ≥ 56

99PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

6x - 7 ≤ 2x - 16

100PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

5(x + 2) + 3 ≥ 2x + 13

101PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

5x - 9 < 2(x + 3)

102PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

2 - (x + 8) ≥ 6 - 4x

103PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

x/5 + 3/4 ≤ x/4 + 1

104PRACTICE PROBLEM

Solve the following linear inequality and express the solution set in interval notation. Then, graph the solution set on a number line.

(x - 3)/7 ≥ (x - 2)/8 + 1/28

105PRACTICE PROBLEM

Solve the following compound inequality: 8 < x + 2 < 14

106PRACTICE PROBLEM

Solve the following compound inequality: -5 ≤ x - 4 < 7

107PRACTICE PROBLEM

Solve the following compound inequality: -14 < 3x - 5 ≤ -3

108PRACTICE PROBLEM

Solve the following compound inequality: -9 ≤ (1/3)x - 3 < -6

109PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. |x| ≤ 5

110PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. |x +2| ≤ 3

111PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. |5x -10| < 20

112PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. |3(x +2) +5| ≤ 11

113PRACTICE PROBLEM

Use interval notation to express the solution set of the following absolute value inequality. |x| > 5

114PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. |x +5| ≥ 3

115PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. |2x -9| > 8

116PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. |2 -x/5| > 1

117PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. 5|x +1| -2 ≥ 3

118PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. -|5x -11| ≥ -9

119PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. 2 > |5 -7x|

120PRACTICE PROBLEM

Simplify the given absolute value inequality and use interval notation to express the solution set. 5 < |-3x +5| -2

121PRACTICE PROBLEM

Find all the values of x satisfying the given conditions and use interval notation to represent them.

z₁ = x +1, z₂ = x/2 +4; z₁ -2 ≤ z₂

122PRACTICE PROBLEM

Find all the values of x satisfying the given conditions and use interval notation to represent them. y = 3x + (1 -x) -2; y is at most 5

123PRACTICE PROBLEM

Find all the values of x satisfying the given conditions and use interval notation to represent them. y = 1 +|2 -x| and y > 7

124PRACTICE PROBLEM

Solve the following inequality and graph its solution set: 2|2x - 8| ≥ 16

125PRACTICE PROBLEM

Solve the given inequality using the graph shown. |x+2| ≥ 1

126PRACTICE PROBLEM

The absolute value function of the sum of 2 times a number and 3 is at most 6. Express all the points in interval notation that satisfy the condition.

127PRACTICE PROBLEM

There are two aromatic solutions, with respective concentrations of 37% and 59%. Which among the following cannot be the final concentration of the mixture?

128PRACTICE PROBLEM

Use number line to demonstrate the set : [-3, 4) ⋂ (-2, 7)

129PRACTICE PROBLEM

Use the number line to demonstrate the set : (1, 5] ⋂ [2, 8)

130PRACTICE PROBLEM

Show the given interval on the number line and demonstrate the interval in set-builder notation : (-∞, 3]

131PRACTICE PROBLEM

Find the domain of the following square root function.

√(x/(10x - 5) - 3)

132PRACTICE PROBLEM

Find the domain of the following square root function.

√(5x/(x + 4) - 4)

133PRACTICE PROBLEM

Find the domain of the following square root function.

f(x) = 6/√(3x² + 10x - 8)

134PRACTICE PROBLEM

Find the domain of the following square root function.

f(x) = √(3x² + 10x - 8)

135PRACTICE PROBLEM

Solve the following polynomial inequality.

x³ ≤ 7x²

Give the solution set in interval notation and graph on a real number line.

136PRACTICE PROBLEM

Solve the following polynomial inequality.

x³ ≥ 7x²

Give the solution set in interval notation and graph on a real number line.

137PRACTICE PROBLEM

Solve the following polynomial inequality.

x³ + 5x² + 25x + 125 > 0

Give the solution set in interval notation and graph on a real number line.

138PRACTICE PROBLEM

Solve the following polynomial inequality.

x³ - 4x² - 16x + 64 < 0

Give the solution set in interval notation and graph on a real number line.

139PRACTICE PROBLEM

Solve the following polynomial inequality.

x³ + 3x² - 9x - 27 ≥ 0

Give the solution set in interval notation and graph on a real number line.

140PRACTICE PROBLEM

Solve the following polynomial inequality.

x³ + 3x² - 16x - 48 ≥ 0

Give the solution set in interval notation and graph on a real number line.

141PRACTICE PROBLEM

Solve the following polynomial inequality.

(5 - x)²(x - 13/2) < 0

Give the solution set in interval notation and graph on a real number line.

142PRACTICE PROBLEM

Solve the following polynomial inequality.

x(11 - x)(x - 13) ≤ 0

Give the solution set in interval notation and graph on a real number line.

143PRACTICE PROBLEM

Solve the following polynomial inequality.

x(12 - x)(x - 17) ≤ 0

Give the solution set in interval notation and graph on a real number line.

144PRACTICE PROBLEM

Solve the following polynomial inequality.

(x + 4)(x + 5)(x + 6) ≥ 0

Give the solution set in interval notation and graph on a real number line.

145PRACTICE PROBLEM

Solve the following polynomial inequality.

(x - 4)(x - 5)(x - 6) ≥ 0

Give the solution set in interval notation and graph on a real number line.

146PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: x/(x - 8) > 0

147PRACTICE PROBLEM

Solve the following polynomial inequality.

25x² - 30x + 9 ≥ 0

Give the solution set in interval notation and graph on a real number line.

148PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (2x + 7)/(8 - 4x) ≥ 0

149PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (8 - 4x)/(5x + 9) ≤ 0

150PRACTICE PROBLEM

Solve the following polynomial inequality.

36x² - 132x + 121 < 0

Give the solution set in interval notation and graph on a real number line.

151PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (-x - 6)/(x + 3) ≤ 0

152PRACTICE PROBLEM

Solve the following polynomial inequality.

x² ≤ 8x + 6

Give the solution set in interval notation and graph on a real number line.

153PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (-x + 5)/(x - 7) ≥ 0

154PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (x + 7)/(x + 9) < 0

155PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (x - 2)/(x + 6) > 0

156PRACTICE PROBLEM

Using a graphing utility, solve the following inequality: 1/(x + 4) ≤ 2/(x + 8)

157PRACTICE PROBLEM

Solve the following polynomial inequality.

x² ≤ 6x - 6

Give the solution set in interval notation and graph on a real number line.

158PRACTICE PROBLEM

Using a graphing utility, solve the following inequality: (x - 6)/(x - 2) ≤ 0

159PRACTICE PROBLEM

Using a graphing utility, solve the following inequality: x³ + 5x² - 2x - 24 > 0

160PRACTICE PROBLEM

Using a graphing utility, solve the following inequality: 4x² + 2x - 6 ≤ 0

161PRACTICE PROBLEM

Solve the following polynomial inequality.

- 4x² + 20x ≥ 0

Give the solution set in interval notation and graph on a real number line.

162PRACTICE PROBLEM

Solve the following polynomial inequality.

9x² - 4x ≤ 0

Give the solution set in interval notation and graph on a real number line.

163PRACTICE PROBLEM

Solve the following polynomial inequality.

4x² + 7x > 0

Give the solution set in interval notation and graph on a real number line.

164PRACTICE PROBLEM

Solve the following polynomial inequality.

x² + 19x < 0

Give the solution set in interval notation and graph on a real number line.

165PRACTICE PROBLEM

Using a graphing utility, solve the following inequality: x² + 4x - 21 > 0

166PRACTICE PROBLEM

Solve the following polynomial inequality.

x² - 11x ≥ 0

Give the solution set in interval notation and graph on a real number line.

167PRACTICE PROBLEM

Solve the following polynomial inequality.

10x² + 5 ≥ 10x

Give the solution set in interval notation and graph on a real number line.

168PRACTICE PROBLEM

Solve the following polynomial inequality.

6x ≤ 4 - 10x²

Give the solution set in interval notation and graph on a real number line.

169PRACTICE PROBLEM

Solve the following polynomial inequality.

5x² + 8x < - 3

Give the solution set in interval notation and graph on a real number line.

170PRACTICE PROBLEM

For the given inequality, find x and graph its corresponding solution set using a real number line. (2x - 10)/(x + 2) ≤ 2

171PRACTICE PROBLEM

For the given inequality, find x and graph its corresponding solution set using a real number line. 2x²- 11x - 40 ≥ 0.

172PRACTICE PROBLEM

For the given inequality, find x and graph its corresponding solution set using a real number line. x²- 12x + 20 < 0

173PRACTICE PROBLEM

Find the solution for the given quadratic inequality. Express the answer in interval notation.

x² - x - 20 < 0

174PRACTICE PROBLEM

Find the solution for the given quadratic inequality. Express the answer in interval notation.

x² - 17x + 60 < 0

175PRACTICE PROBLEM

Find the solution for the given quadratic inequality. Express the answer in interval notation.

4x² - 29x ≥ 63

176PRACTICE PROBLEM

Find the solution for the given quadratic inequality. Express the answer in interval notation.

5x² + x ≥ 6

177PRACTICE PROBLEM

Find the solution for the given quadratic inequality. Express the answer in interval notation.

-x² + 6x + 1 ≥ 0

178PRACTICE PROBLEM

Find the solution for the given quadratic inequality. Express the answer in interval notation.

-x² + 2x + 10 > 0

179PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = 3x(x - 3)(x - 4) given below. Express the answer in interval notation.

3x(x - 3)(x - 4) = 0

180PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = 3x(x - 3)(x - 4) given below. Express the answer in interval notation.

3x(x - 3)(x - 4) < 0

181PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = 3x(x - 3)(x - 4) given below. Express the answer in interval notation.

3x(x - 3)(x - 4) > 0

182PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = 3x(x - 3)(x - 4) given below. Express the answer in interval notation.

3x(x - 3)(x - 4) ≥ 0

183PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = [3(x-5)]/[(x - 4)(x - 6)] given below. Express the answer in interval notation.

[3(x-5)]/[(x - 4)(x - 6)] = 0

184PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = [3(x-5)]/[(x - 4)(x - 6)] given below. Express the answer in interval notation.

[3(x-5)]/[(x - 4)(x - 6)] < 0

185PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = [3(x-5)]/[(x - 4)(x - 6)] given below. Express the answer in interval notation.

[3(x-5)]/[(x - 4)(x - 6)] > 0

186PRACTICE PROBLEM

Find the solution for the following inequality using the graph of f(x) = [3(x-5)]/[(x - 4)(x - 6)] given below. Express the answer in interval notation.

[3(x-5)]/[(x - 4)(x - 6)] ≤ 0

187PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation.

(4x - 3)(6x - 7)(x - 3) < 0

188PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation.

(x - 3)(4x - 3)(6x + 5) ≥ 0

189PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation.

(x - 7)(x - 11)(x - 13) ² ≤ 0

190PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation.

- (x - 7)(x - 11) ²(x - 13) > 0

191PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. (x + 7)³(3x - 2)(x + 11) ≥ 0

192PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. 4x³ - 13x² ≥ 5 - 14x

193PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. x⁴ + 2x³ - 33x² - 90x < 0

194PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. x⁴ - 10x³ + 16 < 40x - 33x²

195PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation.

(x - 2)/(x - 13) > 0

196PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. (x + 2)/(x - 13) > 0

197PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. (4x + 7)/(x - 13) ≤ 0

198PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. (5x + 6)/(x - 17) ≤ 0

199PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. 12/(x - 11) ≥ 3

200PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. 12/(x - 6) ≥ 4

201PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. (x - 11)/(x - 13) < 2

202PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation.

(4x - 6)/(x + 5) > 2

203PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

(x - 7)(x + 9) < 0

204PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

- (x + 5)(x + 6) > 0

205PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

- (x + √5)(x - 11) < 0

206PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

(x - 8)(x + √7) < 0

207PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. x⁵ - 2x² + 24 ≥ 2x⁴ - x³ + 12x

208PRACTICE PROBLEM

For the given inequality expression, solve and write the solution set in interval notation. x⁴ + 54x² + 81 ≥ 12x³ + 108x

209PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

(x - 5)² ≤ 0

210PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

-(x + 11)² ≥ 0

211PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

x² + x - 110 ≤ 0

212PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

x² - 4 > 3x

213PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

3x² + 14 ≤ 23x

214PRACTICE PROBLEM

Provide the solution interval for the given polynomial inequality.

-x(x - 4)(x - 5) ≤ 0

215PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
(x² - 4x- 12) / (x² + 10x + 25) ≤ 0

216PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
1 /(x +12) > 1 /(x -13)

217PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
1 /(x -36) < 1 /(x +36)

218PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
6 /(x - 18) ≥ 3 / x

219PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
6/(x + 17) ≥ 4 /x

220PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
1/(13 - x) > 2 /(17 - x)

221PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
1 /(x² - 16) ≤ 2 /(4 - x)

222PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
1 /(x² - 13x + 12) ≤ 1 /(12 - x)

223PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
(5x- 3)(x +27)<0

224PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
(x- 13)(x-11)(x+21)>0

225PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
(x+19)/(7x+1) < 0

226PRACTICE PROBLEM

Provide the solution set for the given rational inequality in interval notation.
4/(x+23) > 3/(x- 2)

227PRACTICE PROBLEM

Complete the sentence by filling in the blank with the correct words: The degree of a polynomial function with a leading term of 9x⁷ is:

228PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(15x - 2) / (x² + 9) ≥ 0

229PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(11x - 1)/(5x² + 64) < 0

230PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(2 - 13x)² / (4x - 3)³ > 0

231PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(8x - 1)³ / (14 - 3x)² ≤ 0

232PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(5x + 2)(4x - 3) / (x - 9)³ ≥ 0

233PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(3x + 17)(2x - 5) / (2x - 7)³ > 0

234PRACTICE PROBLEM

A cricketer hits a leather ball such that the height (h, in feet) of the ball after the time (t in seconds) is given as h = -8t² + 22t + 2. Estimate the time when the leather ball is at least 14 feet above the ground.

235PRACTICE PROBLEM

Suppose a car is moving with a velocity v = 4t² + 12t - 16. Estimate the time when the velocity of the car is negative. Write the answer in interval notation.

236PRACTICE PROBLEM

Explain why 5 should not be included in the solution set of (18x + 6) / (x - 5) > 0.

237PRACTICE PROBLEM

Explain why -8 is in the solution set of (x + 8) / (3x -5) ≥ 0.

238PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x² - 18x + 77 < 0

239PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x² + 11x - 26 > 0

240PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x² - 18x + 77 > 0

241PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. 3x² - 7x ≤ 20

242PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. 5x² - 8x ≤ 4

243PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x(x - 4) ≤ 32

244PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x(x - 6) < 27

245PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x² ≤ 289

246PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x² > 169

247PRACTICE PROBLEM

From the inequalities given below, the solution set (- ∞, ∞) would only be true for:

248PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

11 / (x + 5) ≥ 2

249PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

6 / (x + 13) ≥ 4 / (x + 13)

250PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

2 / (x + 7) > 9 / (x + 7)

251PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

10 / (5 - x) ≤ 3 / (5 - x)

252PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

5 / (9 + x) ≤ 2 / (9 + x)

253PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

9 / (3x - 1) > -2 / x

254PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

10 / (3 - x) ≥ 8 / (1 - x)

255PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

5 / (x + 4) < 2 / (x + 7)

256PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(x + 12) / (4x - 9) ≤ 1

257PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(x + 8) / (5x + 1) ≤ 2

258PRACTICE PROBLEM

Find the solution set of the following inequality and express it in interval notation:

x² - 5x ≥ 8

259PRACTICE PROBLEM

Find the solution set of the following inequality and express it in interval notation:

(15x + 30) / (x - 7) > 0

260PRACTICE PROBLEM

Find the solution set of the following inequality and express it in interval notation:

(x + 15) / (4x + 9) ≤ 2

261PRACTICE PROBLEM

Find the solution set of the following inequality and express it in interval notation:

(4x - 7) / x - 11 > 0

262PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. 9x² + 6x + 2 ≤ 0

263PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x² - 6x ≤ 6

264PRACTICE PROBLEM

For the following quadratic inequality, solve and express the solution set in interval notation. x² + 6x > - 6

265PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(x - 14) / (x + 22) ≤ 0

266PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(x - 11) / (x - 20) ≤ 0

267PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(x + 18) / (x + 25) ≥ 0

268PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(x + 7) / (x - 18) > 0

269PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(9 - x) / (x + 12) > -1

270PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

(20 - x) / (x + 8) > 1

271PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

20 / (x - 8) ≤ 5

272PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

25 / (x - 3) < 5

273PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

-18 / (3 - x) < 4

274PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

16 /(x + 5) ≥ 4

275PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

12 / (x + 7) > 6

276PRACTICE PROBLEM

Solve the following inequality and express the answer in interval notation:

15 / (1 + 4x) ≤ 6

277PRACTICE PROBLEM

Find the solution set of the following inequality and express it in interval notation:

[(14x + 20) / x] + 2 < 0

278PRACTICE PROBLEM

Find the solution set of the following inequality and express it in interval notation:

4 / (x - 8) ≤ 8 / (x + 9)

279PRACTICE PROBLEM

Find the solution set of the following inequality and express it in interval notation:

11 / (x + 7) > 5 / (x - 2)

280PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: (x - 8)(x + 3) > 0

281PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: (x + 6)(x - 9) > 0

282PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: (x + 4)(x - 9) ≤ 0

283PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: x² + 7x + 10 > 0

284PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: x² - 10x + 25 < 0

285PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: 2x² + x - 15 ≤ 0

286PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: 3x² + 13x < 10

287PRACTICE PROBLEM

Solve the following polynomial inequality and graph the solution set on a number line: 15x² + 2x > 1

288PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (x - 2)/x > 0

289PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: [(x + 6)(x - 4)]/(x + 1) ≤ 0

290PRACTICE PROBLEM

Using a number line, graph the solution set for the following inequality.

|x² + 3x - 25| > 15

291PRACTICE PROBLEM

Using a number line, graph the solution set for the following inequality.

4/(x +4) > 4/(x - 5)

292PRACTICE PROBLEM

Using a number line, graph the solution set for the following inequality.

5/(x + 5) > 10/(x - 5)

293PRACTICE PROBLEM

Using a number line, graph the solution set for the following inequality.

(x² -x - 6)/(x² - 6x + 8) > 0

294PRACTICE PROBLEM

Using the following graph, solve the given inequality.

3x³ - 5x² ≥ 4x - 4

295PRACTICE PROBLEM

Using the following graph, solve the given inequality.

3x³ - 5x² < 4x - 4

296PRACTICE PROBLEM

Using the following graph, solve the given inequality.

1/(5(x + 3)) ≤ - 4/(5(x - 3))

297PRACTICE PROBLEM

Using the following graph, solve the given inequality.

1/(5(x + 3)) > - 4/5((x - 3))

298PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (x - 4)/(x + 4) ≤ 5

299PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: x/(x + 4) ≥ 5

300PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (x + 5)/(x + 1) < 3

301PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: (x + 6)/(3x - 2) ≤ 5

302PRACTICE PROBLEM

Solve the following rational inequality and graph the solution set on a number line: 1/(x - 4) < 1/2

Previous Topic: Choosing a Method to Solve Quadratics

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