Deck 1: Equations and Inequalities

Question 1

Solve the equation.
= -15

A) {-15, 15}
B) {-15}
C) {15}
D) No solution

Answer 1

No solution

Question 2

Solve the equation.
= 12

A) {12, -12}
B) {12}
C) {-12}
D) No solution

Answer 2

{12, -12}

Question 3

Solve the equation.
= 27

A) {18}
B) {-18, 9}
C) {-9, 18}
D) {-9}

Answer 3

{-9, 18}

Question 4

Solve the equation.
= 4.6

A) {1.85}
B) {-0.15, 1.85}
C) {-1.85, 0.15}
D) {0.15, 1.85}

Question 5

Solve the equation.
= 5.0

A) {-0.02}
B) {1.98, 0.02}
C) {-1.98, 0.02}
D) {-0.02, 1.98}

Question 6

Solve the equation.
= 1

A)
B)
C)
D)

Question 7

Solve the equation.
= 1

A)
B)
C)
D)

Question 8

Write an absolute value equation that describes the statement.Any number whose distance from x = 19 on the number line is 2.

A)
B)
C)
D)

Question 9

Write an absolute value equation that describes the statement.Any number whose distance from x = -3 on the number line is 20.

A)
B)
C)
D)

Question 10

Write an absolute value equation that describes the statement.Any number whose distance from x = -12a on the number line is 1.

A)
B)
C)
D)

Question 11

Solve the inequality and express the solution in interval notation.
< 10

A) (-?, 24)
B) (4, 24)
C) (-?, 4) ? (24, ?)
D) (-24, 24)

Question 12

Solve the inequality and express the solution in interval notation.
? 17

A) [-10, 7]
B) (-10, 7)
C) (-?, -10] ? [7, ?)
D) (-?, -10) ? (7, ?)

Question 13

Solve the inequality and express the solution in interval notation.
? 8

A) [-1, 9/7]
B) (-1, 9/7)
C) (-?, 9/7]
D) [-1, ?)

Question 14

Write an inequality that describes the statement any real number at least 2 units from -17.

Question 15

If the average temperature in Chicago is 36 degrees Fahrenheit plus or minus 12 degrees, write an absolute value inequality representing the temperature in Chicago.

Question 16

Solve the inequality and express the solution in interval notation.

A) (-?, -2/3) ? (-2/3, ?)
B) (-2/3, 2/3)
C) [2/3, ?)
D) (-?, -2/3] ? [-2/3, ?)

Question 17

Solve the inequality and express the solution in interval notation.

A) [-21/2, 21/2]
B) [15/2, 21/2]
C) (15/2, 21/2)
D) (-?, 21/2)

Question 18

Solve the equality.

Question 19

Solve the equality.

Question 20

Solve the inequality and express the solution in interval notation.

Question 21

Solve the inequality and express the solution in interval notation.

Question 22

Solve the polynomial inequality and express the solution set in interval notation.

A) (-?, -2] ? [5, ?)
B) (-?, -2) ? (5, ?)
C) (-2, 5)
D) [-2, 5]

Question 23

Solve the polynomial inequality and express the solution set in interval notation.

A)
B)
C)
D)

Question 24

Solve the polynomial inequality and express the solution set in interval notation.

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

Question 25

Solve the polynomial inequality and express the solution set in interval notation.

A) (0, 10)
B) (-?, 0) ? (10, ?)
C) (-?, 0] ? [10, ?)
D) [0, 10]

Question 26

Solve the polynomial inequality and express the solution set in interval notation.

A) (-16, 0)
B) (-?, -16) ? (0, ?)
C) (-?, -16] ? [0, ?)
D) [-16, 0]

Question 27

Solve the polynomial inequality and express the solution set in interval notation.

A) (0, 2)
B) (-?, 0) ? (2, ?)
C) (-?, -2) ? (2, ?)
D) [0, 2]

Question 28

Solve the polynomial inequality and express the solution set in interval notation.

A) (-?, -4) ? (4, ?)
B) (-?, ?)
C) (-4, 4)
D) Empty set

Question 29

Solve the polynomial inequality and express the solution set in interval notation.

A) (-?, -1] ? [1, ?)
B) (-?, ?)
C) [-1, 1]
D) Empty set

Question 30

Solve the polynomial inequality and express the solution set in interval notation.

Question 31

Solve the rational inequality and express the solution set in interval notation.

Question 32

Solve the rational inequality and express the solution in interval notation.

Question 33

Solve the rational inequality.

A)
B)
C)
D)

Question 34

Solve the rational inequality.

A) (-4, 3) ?
B) (-?, -4] ?
C) (-?, -4] ?
D) (-4, 3] ?

Question 35

Solve the rational inequality.

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

Question 36

Solve the polynomial inequality and express the solution set in interval notation.

A) (-3/2, 6/5)
B) [-3/2, 6/5]
C) [-6/5, 3/2]
D) (-6/5, 3/2)

Question 37

Solve the polynomial inequality and express the solution set in interval notation.

A) (-9/7, 3)
B) (-?, -9/7) ? (3, ?)
C) (-?, -9/7] ? (3, ?)
D) (-?, -3) ? (9/7, ?)

Question 38

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

Question 39

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

A)

B)

C)

D)

Question 40

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

Question 41

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

A)

B)

C)

D)

Question 42

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

A)

B)

C)

D)

Question 43

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

A)

B)

C)

D)

Question 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

Solve the rational inequality. Express the answer in interval notation.

Question 49

Rewrite in interval notation.
X ? -14

A) (-?, -14)
B) (-?, -14]
C) [-14, ?)
D) (-14, ?)

Question 50

Rewrite in interval notation.
X > 19

A) (-?, 19)
B) (-?, 19]
C) (19, ?)
D) [19, ?)

Question 51

Rewrite in interval notation.
3 ? x ? 19

A) (3, 19)
B) (3, 19]
C) [3, 19)
D) [3, 19]

Question 52

Rewrite in interval notation.
-4 < x ? 14

A) (-4, 14)
B) (-4, 14]
C) [-4, 14)
D) [-4, 14]

Question 53

Rewrite in interval notation.
-15 ? x ? -15

A) (-15, -15)
B) {-15}
C) [-15, -15)
D) (-?, ?)

Question 54

Rewrite in set notation.
(-10, -9]

A)
B)
C)
D)

Question 55

Rewrite in set notation.
[-15, 8]

A)
B)
C)
D)

Question 56

Solve and express solution in interval notation.
3x - 27 ? -12

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

Question 57

Solve and express solution in interval notation.
-4x < 8

A) [-2, ?)
B) (-2, ?)
C) (-?, -2)
D) (-?, -2]

Question 58

Solve and express solution in interval notation.
4 - 5(x + 9) < 9

A) [-10, ?)
B) (-10, ?)
C) (-?, 10)
D) (-?, 10]

Question 59

Solve and express in interval notation.
-6 < 3+ 5x < 12

A) (-?, 9/5)
B) [-9/5, 9/5]
C) (-9/5, 9/5)
D) [-9/5, ?)

Question 60

Solve and express in interval notation.
6 < 18 - 3x < 15

A) [1, 4]
B) (1, 4)
C) (4, 1)
D) (-4, -1)

Question 61

Write the indicated set as a single interval, if possible.
[-15, 13) ∪ (-5, 54)

Question 62

Solve and express solution in interval notation.
-3 < 7 - x ≤ 10

Question 63

In your general physics class, your first four test scores are 86, 89, 79, and 73. What is the lowest score you can get on the fifth test to earn a B or better for the course? Assume each test is of equal weight and a B is any score greater than or equal to 80.

Question 64

Typical markup on new cars is 13%-24%. If the sticker price is $20,499, write an inequality that gives the range of the invoice price (what the dealer paid the manufacturer for the car). Round to the nearest cent.

A) $16,531.45 < invoice price < $18,140.71
B) $23,562.07 < invoice price < $26,972.37
C) $17,834.13 < invoice price < $15,579.24
D) $15,579.24 < invoice price < $23,163.87

Question 65

Write the indicated set as a single interval, if possible.
[-16, 19) ∩ (7, 51)

Question 66

Write the indicated set as a single interval, if possible.Write the indicated set as a single interval, if possible.[-16, ∞) ∩ (1, 60)

Question 67

Solve and express solution in interval notation.

Question 68

Write the inequality illustrated on the number line.

Question 69

Write the inequality illustrated on the number line.

Question 70

Write the inequality illustrated on the number line.

Question 71

Express the region represented on the number line in interval notation.

Question 72

Express the region represented on the number line in interval notation.

Question 73

Express the region represented on the number line in interval notation.

Question 74

Solve the radical equation.
= 9

A) {19}
B) {71}
C) {10 + }
D) {91}

Question 75

Solve the radical equation.
= 7

A) {11/4}
B)
C) {53/4}
D) {45/4}

Question 76

Solve the radical equation.
= -3

A) {31/5}
B) {-31/5}
C) {5/5}
D) {-5/5}

Question 77

Solve the radical equation.
Y = 10

A) {0}
B) {10}
C) {100}
D) {0, 100}

Question 78

Solve the radical equation.
= y - 10

A) {10}
B) {10, -10}
C) {0}
D) {4.8}

Question 79

Solve the radical equation.
X = 5

A) {25}
B) {-25, 25}
C) {-25}
D) {-5, 5}

Question 80

Introduce a u - substitution that transforms the equation to quadratic form. Do not solve.

A) u =
B) u = x
C) u =
D) u =