Deck 1: Equations, Inequalities, and Modeling

Question 1

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
3(8t + 10) = 6(2t + 3)

A) Identity, {all real numbers}
B) Conditional, {-1}
C)
D) Conditional, {-4}

Answer 1

Conditional, {-1}

Question 2

Decide whether the given number is a solution to the equation preceding it.
7p + 5p - 4 = 32; 3

A) No
B) Yes

Answer 2

Yes

Question 3

Decide whether the given number is a solution to the equation preceding it.
9m + 8 = 46; 4

A) No
B) Yes

Answer 3

No

Question 4

Solve the equation.
4z + 12 = 3z + 4

A) {16}
B) {-16}
C) {-8}
D) {8}

Question 5

Decide whether the given number is a solution to the equation preceding it.

A) No
B) Yes

Question 6

Solve the equation.
3(y + 3) = 4(y - 8)

A) {23}
B) {41}
C) {-23}
D) {-41}

Question 7

Solve the equation.
10y = 3y + 8 + 6y

A) {8}
B) {80}
C) {-8}
D) {-80}

Question 8

Solve the equation.
4(2z - 2) = 7(z + 4)

A) {36}
B) {24}
C) {-20}
D) {20}

Question 9

Solve the equation.

A)
B) 45
C) - 6
D) 9

Question 10

Decide whether the given number is a solution to the equation preceding it.

A) Yes
B) No

Question 11

Decide whether the given number is a solution to the equation preceding it.
p - 3 = 4; 7

A) Yes
B) No

Question 12

Solve the equation.
13(8c - 2) = 4c - 2

A)
B)
C)
D)

Question 13

Solve the equation.
-5x + 7(2x - 2) = -1 - 4x

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

Question 14

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
16m + 4 = 2(5m + 29)

A) Conditional, {-10}
B) Identity, {all real numbers}
C)
D) Conditional, {9}

Question 15

Decide whether the given number is a solution to the equation preceding it.
6y + 9(y - 6) = 81; 9

A) No
B) Yes

Question 16

Decide whether the given number is a solution to the equation preceding it.

A) Yes
B) No

Question 17

Solve the equation.
9x - 8x = 17

A) {-17}
B) {17}
C) {0}
D)

Question 18

Solve the equation.
-5a + 5 + 6a = 14 - 21

A) {40}
B) {-40}
C) {12}
D) {-12}

Question 19

Decide whether the given number is a solution to the equation preceding it.
p + 11 = 25; 14

A) Yes
B) No

Question 20

Solve the equation.

A)
B)
C) - 12
D)

Question 21

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A)
B)
C)
D)

Question 22

Use a calculator to help solve the equation. Round approximate answers to three places.
x + 285.992 = 226.288

A) {0.791}
B) {1.264}
C) {-59.704}
D) {512.28}

Question 23

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
4(4f - 18) = 16f - 72

A) Conditional, {1}
B)
C) Conditional, {all real numbers}
D) Identity, {all real numbers}

Question 24

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

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

Question 25

Use a calculator to help solve the equation. Round approximate answers to three places.
-355.825x = -478.128

A) {1.344}
B) {170,129.896}
C) {-122.303}
D) {0.744}

Question 26

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A)
B) Conditional, {3}
C)
D)

Question 27

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A)
B)
C) Identity, {all real numbers}
D) Conditional, {42}

Question 28

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A)
B) Conditional, {0}
C) Conditional, - 3
D) Identity, {all real numbers}

Question 29

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A) Conditional, {8}
B)
C)
D) Identity, {all real numbers}

Question 30

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A) Conditional, {-8}
B) Identity, {all real numbers}
C)
D)

Question 31

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
-25s - 45 + 5(5s + 10) = 0

A) Inconsistent, {all real numbers}
B) Identity, {all real numbers}
C)
D)

Question 32

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
20k + 71 = 4(5k + 17)

A) Inconsistent, {all real numbers}
B)
C) Identity, {all real numbers}
D)

Question 33

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A)
B) Identity, {all real numbers}
C) Conditional, {5}
D) Conditional, {-5}

Question 34

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A) Identity, {all real numbers}
B)
C) Conditional, {5}
D) Conditional, {-6}

Question 35

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

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

Question 36

Use a calculator to help solve the equation. Round approximate answers to three places.
-251.031 = 621.153 + x

A) {-2.474}
B) {-872.184}
C) {-0.404}
D) {370.122}

Question 37

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
7x + 10x = -9x

A) Conditional, {26}
B) Identity, {all real numbers}
C)
D) Conditional, {0}

Question 38

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
2(4g - 8) - 8g + 16 = 0

A) Conditional, {1}
B)
C) Identity, {all real numbers}
D) Conditional, {all real numbers}

Question 39

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A) Conditional, {-8}
B)
C) Identity, {all real numbers}
D)

Question 40

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.

A)
B)
C)
D) Identity, {all real numbers}

Question 41

Solve the equation.

A) {72}
B) {-72}
C) {-69}
D) {69}

Question 42

Solve the absolute value equation.

A) {0, 4}
B) {0}
C) {-4, 4}
D) {-4, 0}

Question 43

Use a calculator to help solve the equation. Round approximate answers to three places.

A) {-0.312}
B) {-175,566.36}
C) {-3.206}
D) {-516.292}

Question 44

Solve the equation.

A)
B)
C)
D)

Question 45

Solve the equation.
-3.8q + 1.2 = -25.8 - 1.1q

A) {7.4}
B) {10}
C) {-30}
D) {7.1}

Question 46

Solve the absolute value equation.

A)
B)
C)
D)

Question 47

Use a calculator to help solve the equation. Round approximate answers to three places.
-2.7q + 1.4 = -12.1 - 1.2q

A) {5.000}
B) {-15}
C) {9}
D) {5.444}

Question 48

Use a calculator to help solve the equation. Round approximate answers to three places.

A) {1.183}
B) {-0.317}
C) {0.883}
D) {0.083}

Question 49

Use a calculator to help solve the equation. Round approximate answers to three places.

A)
B) {-1.550}
C) {1.550}
D) {2.950}

Question 50

Solve the absolute value equation.

A) {8}
B) {-8, 0}
C)
D) {8, 0}

Question 51

Solve the equation.
2(x + 2) = 2 - 4(x + 2)

A)
B) {10}
C)
D)

Question 52

Use a calculator to help solve the equation. Round approximate answers to three places.

A) {-1.94}
B) {-1.04}
C) {-2.64}
D) {-2.24}

Question 53

Solve the absolute value equation.

A) {-12, 12}
B) {-4, 12}
C) {-22, 12}
D) {14, 12}

Question 54

Solve the absolute value equation.

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

Question 55

Solve the absolute value equation.

A) {4, -4}
B) {16}
C) {4}
D) {-4}

Question 56

Solve the equation.

A)
B) {-4}
C) {-8}
D) {8}

Question 57

Solve the absolute value equation.
4

A)
B)
C)
D)

Question 58

Solve the absolute value equation.

A)
B)
C)
D)

Question 59

Use a calculator to help solve the equation. Round approximate answers to three places.

A) {-0.307}
B) {-0.378}
C) {0.389}
D) {0.378}

Question 60

Solve the absolute value equation.

A) {82}
B) {82, -58}
C) {-58}
D) {58, -82}

Question 61

Solve the problem.
The temperature of water in a certain lake on a day in October can be determined by using the model y = 15.2 - 0.537x where x is the number of feet down from the surface of the lake and y is the Celsius
Temperature of the water at that depth. Based on this model, how deep in the lake is the water 8 degrees?
(Round to the nearest foot.)

A) 32 ft
B) 69 ft
C) 13 ft
D) 43 ft

Question 62

Solve the formula for the specified variable.
for n

A)
B)
C) n = IR(Ir - E)
D)

Question 63

Solve the equation.

A)
B)
C)
D) Identity, {all real numbers}

Question 64

Solve the equation.

A)
B) Identity, {all real numbers}
C)
D)

Question 65

Solve the problem.
Median family income in Country X between 1990 and 1999 can be modeled by f(x) = 1174.6(x - 1990) + 35,265, where x is the year. Determine symbolically when the median income was $42,092.

A)
B)
C)
D)

Question 66

Solve the problem.
A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x where y is the number of dollars charged and x is the number of minutes the repair person is on the job. How many
Minutes would it take for the cost of repair to reach $120? (Round to the nearest minute.)

A) 118 min
B) 12 min
C) 271 min
D) 187 min

Question 67

Solve the formula for the specified variable.
F = C + 32 for C

A)
B)
C)
D)

Question 68

Solve the formula for the specified variable.
V = Bh for B

A)
B)
C)
D)

Question 69

Solve the problem.
In the following formula, y is the minimum number of hours of studying required to attain a test score of x: y = . How many hours of study are needed to score 87? Round to the nearest hundredth of an hour.

A) 2.26 hr
B) 6.02 hr
C) 101.09 hr
D) 22.60 hr

Question 70

Solve the problem.
The temperature, t, in degrees Fahrenheit, of water being heated is where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

A) 9 min
B) 3 min
C) 6 min
D) 18 min

Question 71

Solve the problem.
Mark has $75 to spend on salmon at $5.00 per pound and/or chicken at $3.00 per pound. If he buys s pounds of salmon and c pounds of chicken, the equation 5s + 3c = 75 must be satisfied. How much salmon did Mark buy if
He bought 5 pounds of chicken?

A) 12 lb
B) 16 lb
C) 19 lb
D) 17 lb

Question 72

Solve the formula for the specified variable.
A = bh for b

A)
B)
C)
D)

Question 73

Solve the formula for the specified variable.
S = for h

A) h = S - r
B)
C)
D)

Question 74

Solve the formula for the specified variable.
P = s

A)
B)
C)
D)

Question 75

Solve the problem.
When going more than 38 miles per hour, the gas mileage of a certain car fits the model y = 43.81 - 0.395x where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what
Speed will the car average 15 miles per gallon? (Round to nearest whole number.)

A) 98 mph
B) 48 mph
C) 149 mph
D) 73 mph

Question 76

Solve the equation.

A) {-1}
B) {1}
C) {-20}
D)

Question 77

Solve the problem.
Yearly sales at a certain department store follow the model y = 85 - 13.254x where y is the total sales in thousands of dollars and x is the number of years after 1992. In what year will the sales first be less than
$35,000?

A) 1996
B) 1995
C) 1990
D) 1989

Question 78

Solve the equation.

A)
B)
C)
D)

Question 79

Solve the equation.

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

Question 80

Solve the problem.
Suppose a cost-benefit model is given by , where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 40% to the nearest dollar.

A) $666
B) $1760
C) $2933
D) $4400