Deck 10: Inequalities in One and Two Variables

Question 1

Solve the inequality and graph the solution on the number line.

A)
B)
C)
D)

Answer 1

Question 2

Solve the problem.
Greg is opening a car wash. He estimates his cost equation as C = 6000 + 0.06x and his revenue equation as R = 1.95x, where x is the number of cars washed in a six month period. Find the minimum number of cars that
Need to be washed in a six month period to make a profit.

A) 31,747 cars
B) 2175 cars
C) 318 cars
D) 3175 cars

Answer 2

3175 cars

Question 3

Solve the inequality and graph the solution on the number line.

A)
B)
C)
D)

Answer 3

Question 4

Solve the inequality.
a - 2 < -6

A) a < -4
B) a > -4
C) a > -8
D) a < -8

Question 5

Solve the inequality and give the solution in interval notation.
a - 5 < -9

A)
B)
C)
D)

Question 6

Solve the inequality and graph the solution on the number line.

A)
B)
C)
D)

Question 7

Solve the inequality.

A)
B) x < -6
C) x > -6
D)

Question 8

Solve the inequality and graph the solution on the number line.

A)
B)
C)
D)

Question 9

Solve the inequality.
2x + 8 < 20

A) x > 6
B) x < 8
C) x > 8
D) x < 6

Question 10

Solve the inequality and graph the solution on the number line.

A)
B)
C)
D)

Question 11

Solve the problem.
Michael scored 67, 86, and 92 on three algebra tests. What must he score on the fourth test in order to have an average grade of at least 85?

A) 82
B) 95
C) 29
D) 61

Question 12

Solve the inequality and graph the solution on the number line.

A)
B)
C)
D)

Question 13

Solve the inequality.
5z + 3 > 4z + 10

A) z < 7
B) z > 13
C) z > 7
D) z < 13

Question 14

Solve the inequality and give the solution in interval notation.

A)
B)
C)
D)

Question 15

Solve the inequality.

A)
B) x < 1
C)
D) x ≤2

Question 16

Solve the inequality.

A) x < -3
B)
C) x > -3
D)

Question 17

Solve the inequality and graph the solution on the number line.

A)
B)
C)
D)

Question 18

Solve the problem.
Shaundra has $4.20 to make a long distance call at a pay phone.The rates listed on the phone for a long distance call are $1.70 for the first three minutes and $0.25 for each additional minute or portion of a minute. Find the
Maximum number of minutes Shaundra can stay on the line.

A) 17 minutes
B) 2 minutes
C) 10 minutes
D) 13 minutes

Question 19

Solve the inequality and give the solution in interval notation.

A)
B)
C)
D)

Question 20

Solve the inequality and give the solution in interval notation.

A)
B)
C)
D)

Question 21

Solve the inequality and give the solution in interval notation.
-4 < x - 1 4

A) [-5, 3)
B) (-5, 3]
C) (-3, 5]
D) [-3, 5)

Question 22

Find A ᴗ B and A ∩ B for the sets A and B.
A = {2, 3, 4, 5, 6}, B = {3, 5, 7, 9}

A)
B)
C)
D)

Question 23

Solve the problem.
From the Venn diagram, determine the set B.

A) {5, 7}
B) {6, 9}
C) {5, 6, 7, 9}
D) {2, 3, 4, 5, 6, 7, 9}

Question 24

Solve the inequality and give the solution in interval notation.

A)
B)
C)
D)

Question 25

Solve the problem.
The Little Town Dog Club offers a "Puppy Kindergarten" for puppies in their community. In order for a dog to
advance from this introductory class to the first level obedience class, it must consistently demonstrate
knowledge of each of 4 commands. The instructor has the following table in her record book. Let A = the set of dogs who have demonstrated knowledge of Sit/Stay.
Let B = the set of dogs who have demonstrated knowledge of Down/Stay.
Let C = the set of dogs who have demonstrated knowledge of Heel.
Let D = the set of dogs who have demonstrated knowledge of Come.
Give each of the sets A, B, C, and D using roster notation. Determine the set A ∩ B ∩ C ∩ D. Which dogs are ready to
advance to the next level?

Question 26

Find the solution set for the inequality.

A)
B)
C)
D)

Question 27

Solve the inequality and give the solution set.

A)
B)
C)
D)

Question 28

Find the solution set for the inequality.

A) {x|x > - 12}
B) {x|x > 12}
C) {x|x < - 12}
D) {x|x < 12}

Question 29

Find A ᴗ B and A ∩ B for the sets A and B.

A)
B)
C)
D) A

Question 30

Find the solution set for the inequality.
-5c - 6 -6c - 8

A) -14}
B) -2}
C) -2}
D) {c|c < -2}

Question 31

Solve the inequality and give the solution in interval notation.

A) [3, 5)
B) (3, 5]
C) (-5, -3]
D) [-5, -3)

Question 32

Solve the problem.
The table shows the students who had a score of 80 or higher on the first two tests in a chemistry class. (Note: Every student in the class had a different first name.) Find the set of students who had a score of 80 or higher on the first or second tests.

A) {Fred, Linda, Sue, Earl, Ken, Eloise, Roger, Bill, Cal}
B) {Linda, Ken, Eloise, Roger }
C) {Fred, Ken, Eloise}
D) {Linda, Sue, Earl, Roger, Bill, Cal}

Question 33

Solve the inequality and give the solution in interval notation.

A)
B)
C)
D)

Question 34

Solve the inequality and give the solution in interval notation.

A) [3, 4)
B) (3, 9]
C) (3, 4]
D) [3, 9)

Question 35

Find the solution set for the inequality.
3x + 6 < 27

A) {x|x < 6}
B) {x|x > 7}
C) {x|x > 6}
D) {x|x < 7}

Question 36

Solve the inequality and give the solution in interval notation.

A) [-7, -3]
B) (3, 7)
C) [3, 7]
D) (-7, -3)

Question 37

Find the solution set for the inequality.
-10x + 10 ≤ -2(4x - 13)

A) {x|x > -8}
B) -8}
C) -8}
D) {x|x < -8}

Question 38

Find the solution set for the inequality.
5z - 1 > 4z - 5

A) {z|z < -6}
B) {z|z > -4}
C) {z|z > -6}
D) {z|z < -4}

Question 39

Solve the inequality and give the solution set.

A)
B)
C)
D)

Question 40

Find A ᴗ B and A ∩ B for the sets A and B.
A = {-3, -2, -1}, B = {0, 1, 2}

A)
B)
C)
D)

Question 41

Solve the problem.
A velocity indicates that the object is traveling upward and a velocity 0 indicates that the object is traveling downward. An object is projected upward and Determine the interval when the
Object is traveling downward.

A) [5.8, 32]
B) [5.8, 12]
C) [4.8, 8.8]
D) [0, 5.8]

Question 42

Solve the problem.
The water acidity in a pool is considered normal when the average pH reading of three daily measurements is greater than 7.2 and less than 7.8. If the first two pH reading are 7.28 and 7.88, find the range of pH values for
The third reading that will result in the acidity level being normal.

A) 7.64 < x < 9.44
B) 7.2 < x < 7.8
C) 6.44 < x < 8.24
D) 7.04 < x < 8.84

Question 43

Find the solution set for the equation.
|r + 9| = 7

A) {16, -2}
B) {-16, -2}
C) {2}
D)

Question 44

Provide an appropriate response.
The graph of the solution to on the number line is

A) |x| ≥ 6
B)
C) |x| > 6
D) |x| < 6

Question 45

Find the solution set for the inequality.

A)
B)
C)
D)

Question 46

Find the solution set for the equation.
|6m + 3| = 8

A)
B)
C)
D)

Question 47

Solve the problem.
A velocity indicates that the object is traveling upward and a velocity indicates that the object is traveling downward. An object is projected upward and . Determine the interval when the
Object is traveling upward.

A) [0, 3]
B) [0, 32]
C) [4, 10]
D) [0, 4]

Question 48

Provide an appropriate response.
The graph of the solution to on the number line is

A) |x| ≤5
B) |x| ≥ 5
C) |x| > 5
D) |x| < 5

Question 49

Find the solution set for the inequality.

A)
B)
C)
D)

Question 50

Solve the problem.
Ashley's grades on her first 3 exams are 85, 78, and 79. An average greater than or equal to 80 and less than 90 will result in a final grade of B. What range of grades on Ashley's fourth and final exam will result in a final
Grade of B? The maximum grade is 100.

A)
B)
C)
D) Impossible to get a B.

Question 51

Find the solution set for the equation.
|x| = 10

A) {-10, 10}
B) {100}
C) {-10}
D) {10}

Question 52

Solve the problem.
An Algbra class had 5 tests over the course of the semester. The table gives the average and high score for each of the 5 tests. For what tests was the high score less than 96 or the average less than 70.

A) Test 3
B) Test 2, Test 5
C) Test 1, Test 4
D) Test 2, Test 3, Test 5

Question 53

Solve the inequality and give the solution in interval notation.
-4x > -8 or x + 4 > 1

A)
B)
C)
D) (-3, 2)

Question 54

Provide an appropriate response.
The graph of the solution to on the number line is

A) |x| < 2
B)
C) |x| > 2
D)

Question 55

Solve the inequality and give the solution in interval notation.
4x - 1 > 23 or -x + 9 ≥-9

A) (6, 18]
B) [6, 18)
C)
D)

Question 56

Solve the inequality and give the solution in interval notation.
x + 7 < 4 or -7x < 14

A)
B)
C)
D) (-3, -2)

Question 57

Solve the problem.
An Algebra class had 5 tests over the course of the semester. The table gives the average and high score for each of the 5 tests. For what tests was the high score greater than 97 or the average greater than 80.

A) Test 1, Test 4
B) Test 1, Test 2, Test 4
C) Test 1, Test 2, Test 3, Test 4
D) None

Question 58

Solve the inequality and give the solution set.

A) {x|-3 < x < 3}
B)
C)
D) { }

Question 59

Find the solution set for the equation.
|t + 3| = 0

A) {3, -3}
B) {-3}
C) {3}
D) {0}

Question 60

Provide an appropriate response.
The graph of the solution to on the number line is

A) |x| > 9
B)
C) |x| < 9
D)

Question 61

Find the solution set for the inequality.

A)
B)
C)
D)

Question 62

Find the solution set for the inequality.

A) {y|y < -8 or y > 0}
B) {y|-8 < y < 0}
C) {y|-8 < y < 8}
D) {y|0 < y < 8}

Question 63

Find the solution set for the inequality.

A) {y|y < 0 or y > 6}
B) {y|-6 < y < 6}
C) {y|y < -6 or y > 0}
D) {y|-6 < y < 0}

Question 64

Solve the problem.
A landscaping company sells mulch by the cubic yard. They use a tractor with one yard bucket to put the mulch into trucks or trailers. The actual amount x in each scoop, however, may differ from one cubic yard by as
Much as 0.24 yard. The actual amount x in each scoop, can be described by the inequality |x - 0.24| ≤ 1. What is
The largest amount of mulch you might get when purchasing one cubic yard.

A) 0.76 cubic yd
B) 1.48 cubic yd
C) 1.24 cubic yd
D) 1 cubic yd

Question 65

Find the solution set for the inequality.
|7m + 9| + 8 ≤14

A)
B)
C)
D)

Question 66

Find the solution set for the inequality.
|x| < 1

A) {x|x < -1 or x > 1}
B) {x|x > 1 and x < -1}
C)
D) {x|-1 < x < 1}

Question 67

Find the solution set for the inequality.

A)
B)
C)
D)

Question 68

Solve the inequality and give the solution set.
|x| > -12

A)
B) {12}
C)
D) {x|-12 < x < 12}

Question 69

Find the solution set for the inequality.
|4m + 5| > 4

A)
B)
C)
D)

Question 70

Find the solution set for the equation.

A) {-2, 6}
B) {-6, 2}
C) {-2, 2}
D) {-6, 6}

Question 71

Find the solution set for the equation.
3(x + 1) + 6 = 12

A) {-5, 3}
B) {-5, 0}
C) {-7, 0}
D) {-7, 1}

Question 72

Find the solution set for the inequality.
|

A)
B)
C)
D)

Question 73

Find the solution set for the inequality.
|6m + 3| < 4

A)
B)
C)
D)

Question 74

Find the solution set for the inequality.
|x| > 3

A)
B) {x|-3 < x < 3}
C) {x|x < -3 or x > 3}
D) {x|x > 3 and x < -3}

Question 75

Solve the inequality and give the solution set.

A)
B)
C) {x|-11 < x < 11}
D) {-11}

Question 76

Find the solution set for the equation.
|4(3x + 5)| = 0

A)
B)
C)
D)

Question 77

Find the solution set for the inequality.
|

A)
B)
C)
D)

Question 78

Find the solution set for the inequality.

A) {x|x < -8 or x > 4}
B) {x|-4 < x < 4}
C) {x|x < -4 or x > 8}
D) {x|-4 < x < 8}

Question 79

Solve the problem.
A landscaping company sells 60-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.25 pound. The actual weight of the bag of topsoil, x, can be described by
The inequality |x - 60| ≤0.25. Give the solution of the inequality in interval notation.

A) [59.75, 60.25]
B)
C) [-59.75, 60.25]
D) (59.75, 60.25)

Question 80

Find the solution set for the equation.

A) {6, 0}
B) {-6, 6}
C) {-6, 0}
D)