Deck 2: Linear Equations and Inequalities in One Variable

Question 1

Determine whether the equation in one variable is linear.
7x + 15 = 21

A) linear
B) not linear

Answer 1

linear

Question 2

Solve the equation.
-1 + s = 15

A) {-16}
B) {14}
C) {-14}
D) {16}

Answer 2

{16}

Question 3

Determine whether the equation in one variable is linear.
$$| 14 x | - 29 = 26$$

A) linear
B) not linear

Answer 3

not linear

Question 4

Solve the equation.
11 = b - 19

A) {30}
B) {-8}
C) {8}
D) {-30}

Question 5

Determine whether the equation in one variable is linear.
$$\frac { 6 } { x } = 10$$

A) linear
B) not linear

Question 6

Determine whether the equation in one variable is linear.
$$72.9 x = 8.4$$

A) linear
B) not linear

Question 7

Solve the equation.
x + 15 = 8

A) {23}
B) {7}
C) {-23}
D) {-7}

Question 8

Solve the equation.
$$x + \frac { 1 } { 6 } = \frac { 5 } { 6 }$$

A) $\{ 1 \}$
B) $\left\{ \frac { 4 } { 5 } \right\}$
C) $\left\{ \frac { 1 } { 2 } \right\}$
D) $\left\{ \frac { 2 } { 3 } \right\}$

Question 9

Determine whether the equation in one variable is linear.
$$3 ( x - 4 ) = 0$$

A) linear
B) not linear

Question 10

Determine whether the equation in one variable is linear.
$$\frac { x } { 11 } + 26 = 15$$

A) linear
B) not linear

Question 11

Determine whether the equation in one variable is linear.
$$| x + 2 | = 6$$

A) linear
B) not linear

Question 12

Determine whether the equation in one variable is linear.
$$x ^ { 2 } - 2 = 9$$

A) linear
B) not linear

Question 13

Determine whether the equation in one variable is linear.
$$\sqrt { 2 } x + \pi = 0 . \overline { 6 }$$

A) linear
B) not linear

Question 14

Determine whether the equation in one variable is linear.
$$2 x = 5 x ^ { 3 }$$

A) linear
B) not linear

Question 15

Solve the equation.
$$\frac { 1 } { 2 } + x = 3$$

A) $\left\{ \frac { 7 } { 2 } \right\}$
B) $\{ 5 \}$
C) $\{ 1 \}$
D) $\left\{ \frac { 5 } { 2 } \right\}$

Question 16

Determine whether the equation in one variable is linear.
x - 2 = 12

A) linear
B) not linear

Question 17

Solve the equation.
a - 13 = -2

A) {11}
B) {15}
C) {-15}
D) {-11}

Question 18

Determine whether the equation in one variable is linear.
$$6 \sqrt { x } - 3 = 0$$

A) linear
B) not linear

Question 19

Solve the equation.
x + 5 = -18

A) {13}
B) {23}
C) {-23}
D) {-13}

Question 20

Solve the equation.
-19 = b - 11

A) {-30}
B) {30}
C) {8}
D) {-8}

Question 21

Solve the equation.
-6b + 3 + 4b = -3b + 8

A) {5}
B) {8}
C) {-3}
D) {-8}

Question 22

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
The cost of having a car towed is given by the formula C = 3x + 50, where C is in dollars and x is the number of miles the car is towed. Find the cost of having a car towed 14 miles.

A) $92
B) $42
C) $53
D) $82

Question 23

Solve the equation.
10y = 4y + 4 + 5y

A) {40}
B) {4}
C) {-4}
D) {-40}

Question 24

Solve the equation.
15x - 4 - 9x = 26

A) {8}
B) {5}
C) {6}
D) {3}

Question 25

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
If 239 is subtracted from a number, the result is 715.

A) x - 239 = 715; 954
B) x + 715 = 239; -476
C) x - 239 = 715; -954
D) x + 239 = 715; 476

Question 26

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
The sum of a number and forty-four is fifty.

A) x - 44 = 50; 94
B) x + 44 = 50; 6
C) 44x = 50; 1.14
D) x ÷ 44 = 50; 2200

Question 27

Solve the equation.
$2.1 + x = 17.6$

A) $\{ 15.5 \}$
B) $\{ 19.2 \}$
C) $\{ 19.7 \}$
D) $\{ 15 \}$

Question 28

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
If 251 is added to a number, the result is 484.

A) 251 + x = 484; 233
B) 251 + x = 484; -735
C) x - 251 = 484; 735
D) x + 251 = 484; -233

Question 29

Solve the equation.
$$x - \frac { 1 } { 4 } = \frac { 1 } { 16 }$$

A) $\left\{ - \frac { 21 } { 64 } \right\}$
B) $\left\{ - \frac { 1 } { 8 } \right\}$
C) $\left\{ - \frac { 5 } { 16 } \right\}$
D) $\left\{ \frac { 5 } { 16 } \right\}$

Question 30

Solve the equation.
-5a + 5 + 6a = 13 - 26

A) {-44}
B) {18}
C) {44}
D) {-18}

Question 31

Solve the equation.
-8.2 + 4x - 6.3 + 5x - 2.1 = 5.7 + 10x + 1.3

A) {-23.6}
B) {9.6}
C) {-9.6}
D) {23.6}

Question 32

Solve the equation.
$$- \frac { 1 } { 2 } + z = \frac { 3 } { 8 }$$

A) $\left\{ \frac { 7 } { 8 } \right\}$
B) $\left\{ \frac { 1 } { 2 } \right\}$
C) $\left\{ - \frac { 7 } { 8 } \right\}$
D) $\left\{ \frac { 2 } { 5 } \right\}$

Question 33

Solve the equation.
-23.4 - x = 15.6

A) {39}
B) {-7.8}
C) {7.8}
D) {-39}

Question 34

Solve the equation.
2(2z - 5) = 3(z + 5)

A) {7}
B) {5}
C) {-5}
D) {25}

Question 35

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
Twenty-nine increased by a number equals fifty-two.

A) 29 + x = 52; 23
B) 29x = 52; 1.79
C) 29 - x = 52; -23
D) 29 + 52 = x; 81

Question 36

Solve the equation.
$$4 ( y + 7 ) = 5 ( y - 4 )$$

A) $\{ - 48 \}$
B) $\{ 48 \}$
C) $\{ - 8 \}$
D) $\{ 8 \}$

Question 37

Solve the equation.
$$13 + 9 p = 10 p$$

A) $\{ 13 \}$
B) $\{ 9 \}$
C) $\{ - 13 \}$
D) $\{ - 6 \}$

Question 38

Solve the equation.
$$x + \frac { 1 } { 2 } = - \frac { 1 } { 4 }$$

A) $\left\{ - \frac { 3 } { 4 } \right\}$
B) $\left\{ - \frac { 7 } { 8 } \right\}$
C) $\left\{ - \frac { 1 } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 3 } \right\}$

Question 39

Solve the equation.
$$9 y = 8 y - 2.6$$

A) $\{ 2.6 \}$
B) $\{ - 2.6 \}$
C) $\{ - 19.6 \}$
D) $\{ 9 \}$

Question 40

Solve the equation.
$$14 x - 9 = 6 x + 15$$

A) $\{ 1 \}$
B) $\{ 3 \}$
C) $\{ 4 \}$
D) $\{ 6 \}$

Question 41

Solve the equation using the multiplication property of equality.
$$- 42 x = 36$$

A) $\left\{ \frac { 7 } { 6 } \right\}$
B) $\left\{ \frac { 6 } { 7 } \right\}$
C) $\left\{ - \frac { 6 } { 7 } \right\}$
D) $\left\{ - \frac { 7 } { 6 } \right\}$

Question 42

Solve the equation using the multiplication property of equality.
$$\frac { \mathrm { v } } { - 4 } = 4$$

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

Question 43

Solve the equation using the multiplication property of equality.
$$- 8 x = - 56$$

A) $\{ 7 \}$
B) $\{ 2 \}$
C) $\{ 48 \}$
D) $\{ - 48 \}$

Question 44

Solve the equation using the multiplication property of equality.
$- 11 x + x = - 80$

A) $\{ 9 \}$
B) $\{ - 9 \}$
C) $\{ - 8 \}$
D) $\{ 8 \}$

Question 45

Solve the equation using the multiplication property of equality.
$$\frac { 1 } { 16 } a = 0$$

A) $\{ 16 \}$
B) $\{ 0 \}$
C) $\{ - 16 \}$
D) $\{ 1 \}$

Question 46

Solve the equation using the multiplication property of equality.
$11 \mathrm { x } = 0$

A) $\{ - 11 \}$
B) $\{ 0 \}$
C) $\{ 1 \}$
D) $\{ 11 \}$

Question 47

Solve the equation using the multiplication property of equality.
$$56 = - \frac { 8 } { 9 } x$$

A) $\left\{ - \frac { 496 } { 9 } \right\}$
B) $\{ - 63 \}$
C) $\left\{ - \frac { 512 } { 9 } \right\}$
D) $\left\{ - \frac { 448 } { 9 } \right\}$

Question 48

Solve the equation using the multiplication property of equality.
7a = -56

A) {-8}
B) {-63}
C) {1}
D) {63}

Question 49

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
The amount of water in a leaky bucket is given by the formula f = 125 - 8t, where f is in ounces and t is in minutes. Find the amount of water in the bucket after 2 minutes.

A) 16 oz
B) 109 oz
C) 117 oz
D) 141 oz

Question 50

Solve the equation using the multiplication property of equality.
$$- \frac { n } { 3 } = - 2$$

A) $\{ 6 \}$
B) $\{ - 5 \}$
C) $\{ - 6 \}$
D) $\{ 5 \}$

Question 51

Solve the equation.
-z = -5

A) {5}
B) {0}
C) {-1}
D) {-5}

Question 52

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
The monthly cost of a certain long distance service is given by the formula C = 0.08t + 6.95 where C is in dollars and t is the amount of time in minutes called in a month. Find the cost of calling long distance for 160 minutes in
A month.

A) $18.75
B) $22.95
C) $19.75
D) $12.80

Question 53

Solve the equation using the multiplication property of equality.
$$\frac { 3 } { 4 } x = 21$$

A) $\left\{ \frac { 63 } { 4 } \right\}$
B) $\left\{ \frac { 81 } { 4 } \right\}$
C) $\left\{ \frac { 87 } { 4 } \right\}$
D) $\{ 28 \}$

Question 54

Solve the equation using the multiplication property of equality.
$$\frac { 1 } { 9 } x = - 8$$

A) $\{ - 1 \}$
B) $\{ 1 \}$
C) $\{ - 72 \}$
D) $\{ 0 \}$

Question 55

Solve the equation using the multiplication property of equality.
$$\frac { n } { 4 } = 5$$

A) $\{ 9 \}$
B) $\{ 1 \}$
C) $\{ 8 \}$
D) $\{ 20 \}$

Question 56

Solve the equation using the multiplication property of equality.
$$3 x + 19 x = 15$$

A) $\left\{ \frac { 15 } { 22 } \right\}$
B) $\{ 330 \}$
C) $\left\{ \frac { 22 } { 15 } \right\}$
D) $\{ - 7 \}$

Question 57

Solve the equation using the multiplication property of equality.
$$8 x = 48$$

A) $\{ 384 \}$
B) $\left\{ \frac { 1 } { 6 } \right\}$
C) $\{ 40 \}$
D) $\{ 6 \}$

Question 58

Solve the equation using the multiplication property of equality.
$$8 x + x = 72$$

A) $\{ 9 \}$
B) $\left\{ \frac { 73 } { 8 } \right\}$
C) $\{ 7 \}$
D) $\{ 8 \}$

Question 59

Solve the equation using the multiplication property of equality.
$$\frac { 2 } { 9 } x = - \frac { 4 } { 9 }$$

A) $\left\{ - \frac { 1 } { 2 } \right\}$
B) $\{ - 4 \}$
C) $\{ 2 \}$
D) $\{ - 2 \}$

Question 60

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
The altitude above sea level of an airplane just after taking off from an airport on a high plateau is given by the formula h = 700t + 3182, where h is in feet and t is the time in minutes since take-off. Find the altitude of the
Airplane after 9 minutes.

A) 9582 ft
B) 9482 ft
C) 6300 ft
D) 9382 ft

Question 61

Solve the equation using both the addition and multiplication properties of equality.
$$6 x - 3 x - 3 = - 2 x$$

A) $\left\{ - \frac { 3 } { 5 } \right\}$
B) $\left\{ \frac { 3 } { 5 } \right\}$
C) $\{ - 3 \}$
D) $\left\{ - \frac { 5 } { 3 } \right\}$

Question 62

Solve the equation using both the addition and multiplication properties of equality.
$$5 x - 8 = 56 - 3 x$$

A) $\{ 8 \}$
B) $\{ 24 \}$
C) $\{ 32 \}$
D) $\{ - 8 \}$

Question 63

Solve the equation using both the addition and multiplication properties of equality.
-4x = 66 + 7x

A) {6}
B) {77}
C) {-5}
D) {-6}

Question 64

Solve the equation using both the addition and multiplication properties of equality.
-3 = -3x + 6

A) {-3}
B) {10}
C) {6}
D) {3}

Question 65

Solve the problem.
Power is the time rate of doing work and is commonly measured in watts. Power is given by the formula $\mathrm { P } = \frac { \mathrm { W } } { \mathrm { t } }$ where P is power, W is work (in joules), and t is time in seconds. If 800 watts of power are used in 27 seconds, how much work (in joules) was done?

A) 3 joules
B) 2160 joules
C) 21,600 joules
D) 30 joules

Question 66

Solve the equation using both the addition and multiplication properties of equality.
10y - 35 = 5y

A) {-7}
B) {7}
C) $\left\{ \frac { 7 } { 3 } \right\}$
D) $\left\{ - \frac { 7 } { 3 } \right\}$

Question 67

Solve the equation using both the addition and multiplication properties of equality.
12x - 7 = 4x + 17

A) {6}
B) {1}
C) {3}
D) {4}

Question 68

Solve the equation using both the addition and multiplication properties of equality.
5n - 8 = 37

A) {9}
B) {44}
C) {40}
D) {15}

Question 69

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
The product of three-fourths and a number is six.

A) $\frac { 3 } { 4 } x = 6 ; 8$
B) $\frac { 3 } { 4 } = 6 x ; \frac { 1 } { 8 }$
C) $\frac { 3 } { 4 } - x = 6 ; \frac { - 21 } { 4 }$
D) $\frac { 3 } { 4 } + x = 6 ; \frac { 21 } { 4 }$

Question 70

Solve the equation.
-x = -14

A) {0}
B) {-14}
C) {-1}
D) {14}

Question 71

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
A number subtracted from eighteen is four.

A) 18 - x = 4; 14
B) 18 + x = 4; -14
C) x - 18 = 4; 22
D) 18 - 4 = x; 14

Question 72

Solve the problem.
The time it takes to travel a given distance at constant speed is given by the formula t = dr , where t is the time, d is the distance, and r is the rate of travel. At 0.7 mile per minute, what distance can be traveled in 30 minutes?

A) 21 mi
B) 4.2 mi
C) 42 mi
D) 10.5 mi

Question 73

Solve the problem.
The time it takes to travel a given distance at constant speed is given by the formula t $= \frac { \mathrm { d } } { \mathrm { r } }$ where t is the time, d is the distance, and r is the rate of travel. At 60 miles per hour, what distance can be traveled in 4 hours?

A) 120 mi
B) 240 mi
C) 480 mi
D) 48 mi

Question 74

Solve the equation using both the addition and multiplication properties of equality.
-10y + 21 = -3y

A) $\left\{ - \frac { 21 } { 13 } \right\}$
B) $\{ - 3 \}$
C) $\left\{ \frac { 21 } { 13 } \right\}$
D) $\{ 3 \}$

Question 75

Solve the equation using both the addition and multiplication properties of equality.
8r + 10 = 34

A) {20}
B) {5}
C) {16}
D) {3}

Question 76

Solve the equation using both the addition and multiplication properties of equality.
-2x - 25 = -57

A) 41
B) {-30}
C) {-16}
D) {16}

Question 77

Solve the problem.
To convert meters to feet, you can use the formula f $\mathrm { f } = \frac { \mathrm { m } } { 0.3038 }$ , where f is the distance in feet and m is the distance in meters. How many meters (to the nearest tenth) is 24 feet?

A) 72.9 m
B) 79.0 m
C) 7.3 m
D) 7.9 m

Question 78

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
If thirty is divided by a number, the result is five.

A) $\frac { 30 } { x } = 5 ; 6$
B) $30 - x = 5 ; 25$
C) $\frac { 30 } { 5 } = x ; 6$
D) $\frac { x } { 30 } = 5 ; 150$

Question 79

Solve the equation using both the addition and multiplication properties of equality.
-13 = 7x + 1

A) {-21}
B) {-2}
C) {-17}
D) {2}

Question 80

Solve the equation using both the addition and multiplication properties of equality.
-12 = -2x + 8

A) {-18}
B) {2}
C) {10}
D) {-14}