Deck 1: Equations and Inequalities

Question 1

Graph the inequality on a number line. x > -1

Answer 1

Question 2

Solve. 5 - 4(3x - 2) = 2 + 3(2x - 5)

A)
B)
C)
D)

Answer 2

Question 3

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. -(9x - 18) + 6x = 20 - 2(x + 1)

A) Identity
B) Contradiction
C) Conditional;
D) Conditional;

Answer 3

Conditional;

Question 4

The following equation is given in ax + b = c form. Solve by identifying the value of a, b, and c, then using the formula . 3x - 4 = -34

A) a = 3; b = 4; c = -34; x = -10
B) a = 3; b = -4; c = -34; x = -10
C) a = 3; b = 4; c = -34; x = 10
D) a = 3; b = -4; c = -34; x = 10

Question 5

At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 35 mph. At 11:00 a.m., a second truck leaves along the same route, traveling at 70 mph. When will the second truck catch up to the first?

A) 1:00 p.m.
B) 4:00 p.m.
C) 3:00 p.m.
D) 2:00 p.m.

Question 6

Solve for y. 3x - 2y = 6

A)
B)
C) y = 3x - 3
D)

Question 7

How much pure antifreeze must be added to 12 gallons of 20% antifreeze to make a 40% antifreeze solution?

A) 2 gallons
B) 4 gallons
C) 6 gallons
D) 8 gallons

Question 8

Solve for y.

Question 9

Identify the equation as linear or nonlinear. If nonlinear, state why. Do not solve.

Question 10

Solve. 0.2(5 - 2.4x) - 3.4 = 0

Question 11

Solve. 16 = 32 -

A) 12
B) 13
C) 14
D) 15

Question 12

Give the total amount of the mix that results and the worth per pound of the mix when 8 pounds of nuts worth $1.20 per pound are mixed with 8 pounds of nuts worth $4.20 per pound.

Question 13

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution.
-4(x - 3) + 5x = x + 12

Question 14

Solve for b. a = bc²

A)
B)
C)
D)

Question 15

Solve for y. w = xyz

Question 16

A consultant traveled 450 miles to attend a meeting, traveling 50 mph hours for the first part of the trip, then increasing to a speed of 60 mph for the second part. If the entire trip took 8 hours, how far did the consultant travel at the faster speed?

Question 17

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution.
-6(x + 3) = -3 + 3(-2x - 5)

Question 18

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. 2x + 10(-x - 7) = -54 - 4(2x + 3)

A) Identity
B) Contradiction
C) Conditional;
D) Conditional;

Question 19

Find two consecutive even integers such that the sum of the smaller integer plus twice the larger integer is 148.

Question 20

Solve. - 5 = - 1

Question 21

Use the following to answer questions :
Determine the intersection and union of sets A, B, and C as indicated, given
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find A C.

A) { }
B) {10, 20}
C) {5, 15, 30, 40}
D) {5, 10, 15, 20, 30, 40}

Question 22

Solve the compound inequality and graph the solution set. -2x - 10 ≤ 2 and 3x < 0

A)
-6 0
B)
-6 0
C)
-6
D)
0

Question 23

Determine the allowable value(s) for the expression. Write your answer in interval notation.

Question 24

Use the following to answer questions :
Express the compound inequality graphically.

A)
3 9
B)
3 9
C)
3 9
D) no solution

Question 25

Determine the allowable value(s) for the expression. Write your answer in interval notation.

A) x $\in$ (-?, 5) $\cup$ (5, ?)
B) x $\in$ (-?, -5) $\cup$ (-5, ?)
C) x $\in$ (-?, 7) $\cup$ (7, ?)
D) x $\in$ (-?, -7) $\cup$ (-7, ?)

Question 26

Use the following to answer questions :
Express the compound inequality graphically.

A)
-3 1
B)
-3 1
C)
-3 1
D)
-3 1

Question 27

Use the following to answer questions :
Express the compound inequality graphically.

A)
-5 1
B)
-5 1
C)
-5 1
D)
-5 1

Question 28

Use the following to answer questions :
Determine the intersection and union of sets A, B, and C as indicated, given
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find A C.

A) { }
B) {10, 20}
C) {5, 15, 30, 40}
D) {5, 10, 15, 20, 30, 40}

Question 29

Determine the domain for the expression. Write your answer in interval notation.

A) x $\in$ (-?, -7) $\cup$ (-7, ?)
B) x $\in$ (-?, -7]
C) x $\in$ (7, ?)
D) x $\in$ [-7, ?)

Question 30

Solve the inequality. Then write the solution set in set notation, number line notation, and interval notation.
9n - 3 ? 3n + 51

Question 31

Use the following to answer questions :

-Express the compound inequality in interval notation.

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

Question 32

Use the following to answer questions :

-Express the compound inequality in interval notation.

A) (4, 9)
B) (-?, 9] $\cup$ [4, ?)
C) (-?, 9) $\cup$ (4, ?)
D) no solution

Question 33

Determine the allowable value(s) for the expression. Write your answer in interval notation.

Question 34

Use the following to answer questions :

-Express the compound inequality in interval notation.

A) [-1, 2)
B) (-1, 2]
C) (-?, -1) $\cup$ [2, ?)
D) (-?, -1] $\cup$ (2, ?)

Question 35

Solve the inequality. Then write the solution set in set notation, number line notation, and interval notation.

Question 36

Use the following to answer questions :
Determine the intersection and union of sets A, B, and C as indicated, given
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find A B.

A) { }
B) {10, 15}
C) {5, 10, 35, 40}
D) {5, 10, 15, 20, 25, 30, 35, 40}

Question 37

Graph the inequality on a number line. -4 ≤ y < 1

A)
B)
C)
D)

Question 38

Solve the compound inequality. -0.2 ≤ 0.7 - x ≤ 1.8

A) -2.5 ≤ x ≤ 0.5
B) -1.1 ≤ x ≤ 0.9
C) -0.9 ≤ x ≤ 1.1
D) no solution

Question 39

Use the following to answer questions :
Determine the intersection and union of sets A, B, and C as indicated, given
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find A B.

A) { }
B) {10, 15}
C) {5, 10, 35, 40}
D) {5, 10, 15, 20, 25, 30, 35, 40}

Question 40

Solve the compound inequality and graph the solution set.
-4(x + 3) ≥ 20 or x - 5 < -2

Question 41

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Question 42

Perform the addition. Write the result in a + bi form.
(5 - 8i) + (6 + 5i)

Question 43

Solve the absolute value inequality. Write your answer in interval notation.
|-5 - x| + 11 < 10

Question 44

Write the complex number in the standard form a + bi and clearly identify the values of a and b.

Question 45

Multiply and write your answer in a + bi form. 4i(1 + 3i)

A) 7i
B) -8i
C) -12 + 4i
D) 12 + 4i

Question 46

Multiply and write your answer in a + bi form.
(5 - i)(4 + 3i)

Question 47

Solve the absolute value inequality. Write solution in interval notation. 3|x + 7| + 9 < 15

A) (- $\infty$ , -15) $\cup$ (1, $\infty$ )
B) (- $\infty$ , -9) $\cup$ (-5, $\infty$ )
C) (-15, 1)
D) (-9, -5)

Question 48

Write the complex number in the standard form a + bi.

A) 1 + i
B) 1 - i
C) 1 + 16i
D) 1 - 16i

Question 49

Write the complex number in the standard form a + bi and clearly identify the values of a and b.
-2

Question 50

Determine the domain for the expression. Write your answer in interval notation.

A) y $\in$ (-?, -4) $\cup$ (-4, ?)
B) y $\in$ (-?, 4]
C) y $\in$ [4, ?)
D) y $\in$ (-?, -4]

Question 51

Perform the subtraction. Write the result in a + bi form. (-5 - 2i) - (-8 - 4i)

A) 3 + 2i
B) 3 - 6i
C) -3i
D) 5i

Question 52

Solve the absolute value equation. Write the solution in set notation. -2|x - 9| + 10 = 2

A) {3, 15}
B) {5, 13}
C) {0, 18}
D) {-2, 20}

Question 53

Solve the absolute value inequality. Write the solution in interval notation. |x + 6| ? 6

A) (- $\infty$ -12) $\cup$ (0, $\infty$ )
B) (- $\infty$ , -12] $\cup$ [0, $\infty$ )
C) (-12, 0)
D) [-12, 0]

Question 54

An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 70%, 64%, and 72% on the first three exams, what score must she get on the fourth exam to receive credit for the course?

A) x ≥ 72%
B) x ≥ 74%
C) x ≥ 76%
D) x ≥ 79%

Question 55

Solve the absolute value inequality. Write the solution in interval notation.
|x + 2| > 9

Question 56

Determine the domain for the expression. Write your answer in interval notation.

A) m $\in$ (-?, -5) $\cup$ (-5, ?)
B) m $\in$ (-?, -5]
C) m $\in$ [-5, ?)
D) m $\in$ (5, ?)

Question 57

Solve the absolute value inequality. Write the solution in interval notation. 3|x + 1| + 9 ? 18

A) (- $\infty$ , -10] $\cup$ [8, $\infty$ )
B) (- $\infty$ , -4] $\cup$ [2, $\infty$ )
C) [-10, 8]
D) [-4, 2]

Question 58

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

A)
B)
C)
D)

Question 59

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

Question 60

Simplify the radical, if possible. If imaginary, rewrite in terms of i and simplify.

A) -6
B) -18
C) -6i
D) 6i

Question 61

Solve using the square root property of equality. Write answers in exact form. If there are no real solutions, so state. (x + 5)² = 3

A)
B)
C)
D) no real solutions

Question 62

Solve using the square root property of equality. Write answers in exact form and approximate form rounded to hundredths. If there are no real solutions, so state.
x² - 50 = 0

Question 63

Solve by completing the square. Write your answer in exact form. x² = 5x + 2

A)
B)
C)
D)

Question 64

Divide and write your answer in a + bi form.

Question 65

Determine whether the equation is quadratic. If so, identify the coefficients a, b, and c. 5 = -2x²

A) a = 0, b = 5, c = -2
B) a = 2, b = 5, c = 0
C) a = 2, b = 0, c = 5
D) not quadratic

Question 66

Fill in the blank so the result is a perfect square trinomial, then factor into a binomial square. x² + 7x + _____

A) ;

B) 49; (x + 7)²
C) ;

D) ;

Question 67

Name the complex conjugate, then find the product. 5 - i

A) 5 + i; 26
B) -5 + i; 26
C) 5 + i; 24
D) -5 + i; 24

Question 68

Fill in the blank so the result is a perfect square trinomial, then factor into a binomial square.
x² - 20x + _____

Question 69

Compute the special product and write your answer in a + bi form. (3 - 2i)(3 + 2i)

A) 5 - 12i
B) 13 + 12i
C) 5
D) 13

Question 70

Compute the special product and write your answer in a + bi form.
(5 + 6i)²

Question 71

Simplify using powers of i. i⁴⁵

A) 1
B) -1
C) i
D) -i

Question 72

Simplify using powers of i. i⁴⁷

A) 1
B) -1
C) i
D) -i

Question 73

Solve by completing the square. x² + 4x = 12

A) x = 2, x = -6
B) x = 2, x = 6
C) x = -2, x = -6
D) x = -2, x = 6

Question 74

Solve using the zero product property. Be sure each equation is in standard form and factor out any common factors before attempting to solve. Check all answers in the original equation. (m + 5)(m + 6) = 6

A) m = -5, m = -6
B) m = 1, m = 0
C) m = -8, m = -3
D) m = 8, m = 3

Question 75

Simplify using powers of i. i⁶⁴

A) 1
B) -1
C) i
D) -i

Question 76

Solve using the square root property of equality. Write answers in exact form. If there are no real solutions, so state. (x - 2)² + 10 = 4

A)
B)
C)
D) no real solutions

Question 77

Divide and write your answer in a + bi form. Check your answer using multiplication.

A)
B)
C)
D)

Question 78

Simplify using powers of i. i⁴⁶

A) 1
B) -1
C) i
D) -i

Question 79

Solve using the zero product property. Be sure each equation is in standard form and factor out any common factors before attempting to solve. Check all answers in the original equation.
8x² + 64x = 0

Question 80

Solve using the square root property of equality. If there are no real solutions, so state.
(x + 4)² = 81