Deck 2: Equations, Inequalities, and Problem Solving

Question 1

Solve the equation.
10=x+3

A) {-7}
B) {7}
C) {13}
D) {-13}

Answer 1

{7}

Question 2

Solve the equation.
y-5=18

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

Answer 2

{23}

Question 3

Determine whether the number is a solution of the equation
$- 12 ; \quad 2 x - 7 = 3 x + 5$

A) Yes
B) No

Answer 3

A

Question 4

Solve the equation.
11 x-27=2 x+27

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

Question 5

Solve the equation.
5 x+7=22

A) {10}
B) {3}
C) {14}
D) {2}

Question 6

Determine whether the number is a solution of the equation
$- 1 ; x - 9 = x - 9$

A) Yes
B) No

Question 7

Determine whether the number is a solution of the equation
$- 1 ; x - 1 = x + 1$

A) Yes
B) No

Question 8

Solve the equation.
4 x-8=7-6 x

A) $\left\{ - \frac { 2 } { 3 } \right\}$
B) $\left\{ \frac { 3 } { 2 } \right\}$
C) $\{ 2 \rangle$
D) $\left\{ \frac { 2 } { 3 } \right\}$

Question 9

Determine whether the number is a solution of the equation
$- 4 ; 2 + 3 x = - 10$

A) Yes
B) No

Question 10

Solve the equation.
4 y+4=8-4 y

A) $\{ - 2 \}$
B) $\{ 0 \}$
C) $\{ 2 \}$
D) $\left\{ \frac { 1 } { 2 } \right\}$

Question 11

Solve the equation.
8(y-7)=10y-56

A) {0}
B) {-56}
C) {-112}
D) {56}

Question 12

Solve the equation.
3(5 x-2)-58=8 x-1

A) {441}
B) {-9}
C) {9}
D) {63}

Question 13

Determine whether the number is a solution of the equation
$7 ; \quad 2 ( x - 8 ) = 16$

A) Yes
B) No

Question 14

Solve the equation.
9 z-2=43

A) {36}
B) {40}
C) {6}
D) {5}

Question 15

Solve the equation.
6=2 x-8

A) {7}
B) {11}
C) {16}
D) {12}

Question 16

Solve the equation.
7 x-6=8(x-2)

A) {10}
B) {22}
C) {-22}
D) {-10}

Question 17

Determine whether the number is a solution of the equation
$- 2 ; 8 - 4 x = 0$

A) Yes
B) No

Question 18

Determine whether the number is a solution of the equation
$- 2 ; \quad x - 22 = 24$

A) Yes
B) No

Question 19

Solve the equation.
-4 x=12

A) {-16}
B) {1}
C) {-3}
D) {16}

Question 20

Determine whether the number is a solution of the equation
$- 30 ; \frac { x } { - 5 } = 6$

A) Yes
B) No

Question 21

Solve the equation.
$\frac { 2 x } { 5 } - \frac { x } { 3 } = 4$

A) {-60}
B) {60}
C) {120}
D) {-120}

Question 22

Solve the equation.
$\frac { x + 9 } { 2 } + \frac { x - 2 } { 4 } = \frac { 19 } { 4 }$

A) {38}
B) {0}
C) {1}
D) $\left\{ \frac { 31 } { 2 } \right\}$

Question 23

Solve the equation.
-63(x+8)=-72(x+7)

A) {0}
B) {-135}
C) { $x \mid X$ is a real number}
D)

Question 24

Solve the equation.
15(5 x-2)=5 x-9

A) $\left\{ \frac { 39 } { 70 } \right\}$
B) $\left\{ - \frac { 3 } { 10 } \right\}$
C) $\left\{ \frac { 21 } { 80 } \right\}$
D) $\left\{ \frac { 3 } { 10 } \right\}$

Question 25

Solve the equation.
4(x+7)=5(x-3)

A) {43}
B) {13}
C) { $x \mid x$ is a real number}
D) $\{ \varnothing \}$

Question 26

Solve the equation.
21.9=-21.7-x

A) {-43.6}
B) {-0.2}
C) {43.6}
D) {0.2}

Question 27

Solve the equation.
4 x-3-6 x=x+13+x

A) {-4}
B) $\left\{ - \frac { 5 } { 0 } \right\}$
C) {4}
D) $\phi$

Question 28

Solve the equation.
(x-8)-(x+2)=9x

A) $\left\{ - \frac { 5 } { 3 } \right\}$
B) $\left\{ - \frac { 5 } { 4 } \right\}$
C) $\left\{ - \frac { 10 } { 9 } \right\}$
D) $\left\{ - \frac { 7 } { 9 } \right\}$

Question 29

Solve the equation.
-5 x+2-6 x-8=8

A) $\{ 14 \}$
B) $\left\{ \frac { 14 } { 11 } \right\}$
C) $\left\{ - \frac { 14 } { 11 } \right\}$
D) $\left\{ - \frac { 18 } { 11 } \right\}$

Question 30

Solve the equation.
-(2 x-5)-(3 x-6)+5=-5(x-1)-(2 x+1)+2

A) {5}
B) {11}
C) $\left\{ - \frac { 5 } { 0 } \right\}$
D) {-5}

Question 31

Solve the equation.
9 x=5(5 x+3)

A) $\left\{ \frac { 5 } { 3 } \right\}$
B) $\left\{ - \frac { 15 } { 16 } \right\}$
C) $\left\{ \frac { 16 } { 15 } \right\}$
D) $\left\{ \frac { 15 } { 16 } \right\}$

Question 32

Solve the equation.
8(y+4)-(7y-9)=-3

A) {44}
B) {16}
C) {38}
D) {-44}

Question 33

Solve the equation.
x-21.9=-13.8

A) {-8.1}
B) {35.7}
C) {-35.7}
D) {8.1}

Question 34

Solve the equation.
$\frac { x } { 3 } - \frac { x } { 7 } = 9$

A) {21}
B) {27}
C) {63}
D) $\left\{ \frac { 189 } { 4 } \right\}$

Question 35

Solve the equation.
$\frac { 15 x } { 4 } + \frac { 3 } { 2 } = \frac { 7 x } { 2 }$

A) {-20}
B) {6}
C) {20}
D) {-6}

Question 36

Solve the equation.
$\frac { x } { 3 } - \frac { x } { 4 } = 6$

A) {24}
B) {12}
C) $\{ 72 \}$
D) {18}

Question 37

Solve the equation.
$\frac { 1 } { 2 } - \frac { x } { 3 } = \frac { 11 } { 6 }$

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

Question 38

Solve the equation.
1.3 x+2.1=0.8 x-2.7

A) {-9.5}
B) {-9.6}
C) {0.104}
D) {-8.64}

Question 39

Solve the equation.
$\frac { x } { 5 } = \frac { x } { 3 } + \frac { 9 } { 5 }$

A) $\left\{ - \frac { 2 } { 27 } \right\}$
B) {0}
C) $\left\{ - \frac { 9 } { 5 } \right\}$
D) $\left\{ - \frac { 27 } { 2 } \right\}$

Question 40

Solve the equation.
-6(z+7)-(-7z-6)=-4

A) {-40}
B) {17}
C) {-32}
D) {32}

Question 41

Write the following as an algebraic expression. Then simplify.
The perimeter of the rectangle with width x and length x + 52.

A) 4 x+52
B) x²+52x
C) 2x+52
D) 4x+104

Question 42

Write the following as an algebraic expression. Then simplify.
The perimeter of the floor plan shown.

A) 2x+18
B) 2x
C) 2x+56
D) 56

Question 43

Write the following as an algebraic expression. Then simplify.
The perimeter of a triangle whose sides are of lengths 5 x, 5 x-5 , and x .

A) 10x -5
B) 25x² -25x
C) 11x -5
D) 5x

Question 44

Solve the equation.
0.01y +0.12(800-y)=0.14y

A) {240}
B) {384}
C) {24}
D) {768}

Question 45

Solve the equation.
3(x+4)+5=3 x+2

A) { $x \mid x$ is a real number }
B) {11}
C)

D) {15}

Question 46

Write the following as an algebraic expression. Then simplify.
The sum of three even consecutive integers if the first integer is y .

A) 3y+6
B) 6
C) 3y+3
D) 3y

Question 47

Write the following as an algebraic expression. Then simplify.
The perimeter of a square with sides of length x-6 .

A) x-24
B) 4x-24
C) 4x-6
D) x²+-12x+36

Question 48

Solve the equation.
$\frac { x + 2 } { 2 } - \frac { 5 x - 12 } { 7 } = 1$

A) $\{ 8 \}$
B) $\{ 4 \}$
C) $\{ - 8 \}$
D) {-24}

Question 49

Solve the equation.
-4(x-6)-66=2 x-6(x+3)

A) {-48}
B) {-84}
C) $\varnothing$
D) { $X \mid X$ is a real number}

Question 50

Solve the equation.
$\frac { 1 } { 5 } ( x + 15 ) - \frac { 1 } { 9 } ( x - 9 ) = x + 7$

A) $\left\{ - \frac { 135 } { 41 } \right\}$
B) $\left\{ - \frac { 495 } { 41 } \right\}$
C) $\left\{ - \frac { 225 } { 41 } \right\}$
D) $\left\{ - \frac { 405 } { 41 } \right\}$

Question 51

Write the following as an algebraic expression. Then simplify.
The sum of three consecutive integers if the last integer is z.

A) 3z-3
B) 3z
C) 3z+3
D) 3z+6

Question 52

Write the following as an algebraic expression. Then simplify.
The total value of money (in cents) of (7x-2) nickels, 6x dimes, and x quarters.

A) (95x-10) cents
B) (120x-2) cents
C) (120x-10) cents
D) (120x+10) cents

Question 53

Solve.
The difference of a number and 8 is the same as 46 less the number. Find the number.

A) 27
B) 19
C) -27
D) -19

Question 54

Solve.
Four times the sum of some number plus 3 is equal to 8 times the number minus 12 .

A) -24
B) 24
C) -6
D) 6

Question 55

Solve the equation.
5(x-1)+x=6(x+1)-11

A) $\varnothing$
B) {0}
C) { $x \mid X$ is a real number}
D) {5}

Question 56

Solve the equation.
3(x+4)-(3 x+12)=0

A) { $x \mid x$ is a real number
B)
C) {4}
D) {0}

Question 57

Solve the equation.
2 x-1-9 x-8=5 x-12 x-12

A) $\varnothing$
B) {-288}
C) {0}
D) { $x \mid x$ is a real number}

Question 58

Solve the equation.
1.8(2-x)=1.6(2-x)

A) {2}
B) {0.4}
C) {0}
D) {34}

Question 59

Solve the equation.
5(x+5)=(5 x+25)

A) {50}
B) { $\{ x \mid x$ is a real number }
C) {0}
D) $\varnothing$

Question 60

Solve the equation.
$\frac { 2 x - 1 } { 6 } + x = \frac { 2 x + 1 } { 2 } + 4$

A) $\{ 14 \}$
B) {6}
C) $\{ - 13 \}$
D) $\left\{ - \frac { 8 } { 3 } \right\}$

Question 61

Solve.
Angle A and angle B are supplementary angles and angle A is $35 ^ { \circ }$ less than four times angle B . Find the measures of angle A and angle B .
$\text { Supplementary Angles }$

A) $\mathrm { A } = 151 ^ { \circ } , \mathrm { B } = 29 ^ { \circ }$
B) $\mathrm { A } = 131.7 ^ { \circ } , \mathrm { B } = 48.3 ^ { \circ }$
C) $\mathrm { A } = 137 ^ { \circ } , \mathrm { B } = 43 ^ { \circ }$
D) $A = 172 ^ { \circ } , B = 8 ^ { \circ }$

Question 62

Solve.
A region consists of 2565 thousand acres of farm land. If 30 % of this land is privately owned, find how may acres are not privately owned.

A) 1795.5 thousand acres
B) 769.5 thousand acres
C) 1795.5 acres
D) 769.5 acres

Question 63

Solve the equation for the specified variable.
d=rt for r

A) $r = \frac { d } { t }$
B) $r = \frac { t } { d }$
C) r=dt
D) r=d-t

Question 64

Solve.
A Promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per munite for all calls. if joe's phone bill was $62 under this promotional deal, how many minuts of phone calls did he make? Round to the nearest interher, if necessary .

A) 9
B) 1540
C) 2
D) 940

Question 65

Solve.
Find the measures of the angles of a triangle if the measure of the first angle is four times the measure of the second angle and the third angle is $30 ^ { \circ }$ more than the second angle.

A) $100 ^ { \circ } , 25 ^ { \circ } , 55 ^ { \circ }$
B) $35 ^ { \circ } , 5 ^ { \circ } , 140 ^ { \circ }$
C) $68 ^ { \circ } , 17 ^ { \circ } , 95 ^ { \circ }$
D) $20 ^ { \circ } , 5 ^ { \circ } , 155 ^ { \circ }$

Question 66

Solve.
The three most prominent buildings in a city, Washington Center, Lincoln Galleria, and Jefferson Square Tower, have a total height of 1800 feet. Find the height of each building if Jefferson Square Tower is three times as tall as Lincoln Galleria and Washington Center is 350 feet taller than Lincoln Galleria.

A) Washington Center: 240 feet
Lincoln Galleria: 80 feet
Jefferson Square Tower: 1480 feet
B) Washington Center: 430 feet
Lincoln Galleria: 80 feet
Jefferson Square Tower: 1290 feet
C) Washington Center: 640 feet
630 feet Lincoln Galleria: 290 feet
Jefferson Square Tower: 870
D) Washington Center: 630 feet
Lincoln Galleria: 210
Jefferson Square Tower: 960 feet

Question 67

Solve.
In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the total number of medals won by each team are three consecutive integers whose sum is 81 and the U.S. won more than China who won more than Romania, how many medals did each team win?

A) U.S.: 29 medals; China: 28 medals; Romania: 27 medals
B) U.S.: 83 medals; China: 82 medals; Romania: 81 medals
C) U.S.: 28 medals; China: 27 medals; Romania: 26 medals
D) U.S.: 26 medals; China: 25 medals; Romania: 24 medals

Question 68

Solve the equation for the specified variable.
I= Prt for P

A) $P = \frac { \mathbf { r } - 1 } { \mathrm { It } }$ .
B) P=r - It
C) $P = \frac { r - I } { 1 + t }$
D) $P = \frac { I } { r t }$

Question 69

Solve.
The president of a certain University makes three times as much money as one of the department heads. If the total of there salaries is $250,000 , find each worker's salary.

A) President salary =$18,750; department heads salary =$6250
B) President salary =$187,500; department heads salary =$62,500
C) President salary =$125,000; department heads salary =$62,500
D) President salary =$62,500; department heads salary =$187,500

Question 70

Solve.
Angle A and angle B are complementary angles and angle A is $2 ^ { \circ }$ more than three times angle B . Find the measures of angle A and angle B .

A) \(\mathrm { A } = 48 ^ { \circ } , \mathrm { B } = 42 ^ { \circ }">\text { Complemenatry Angles }\<img src="https://d2lvgg3v3hfg70.cloudfront.net/TB7570/11ecb57d_b55a_833b_83e2_99214c62db6f_TB7570_00.jpg" alt=" <strong>Solve. Angle A and angle B are complementary angles and angle A is 2 ^ { \circ } more than three times angle B . Find the measures of angle A and angle B . \text { Complemenatry Angles }\ </strong> A) \mathrm { A } = 48 ^ { \circ } , \mathrm { B } = 42 ^ { \circ } B) \mathrm { A } = 68 ^ { \circ } , \mathrm { B } = 22 ^ { \circ } C) \mathrm { A } = 42 ^ { \circ } , \mathrm { B } = 48 ^ { \circ } D) \mathrm { A } = 22 ^ { \circ } , \mathrm { B } = 68 ^ { \circ } " class="answers-bank-image d-block" loading="lazy" ></strong><div>A) \(\mathrm { A } = 48 ^ { \circ } , \mathrm { B } = 42 ^ { \circ }
B) $\mathrm { A } = 68 ^ { \circ } , \mathrm { B } = 22 ^ { \circ }$
C) $\mathrm { A } = 42 ^ { \circ } , \mathrm { B } = 48 ^ { \circ }$
D) $\mathrm { A } = 22 ^ { \circ } , \mathrm { B } = 68 ^ { \circ }$

Question 71

Solve.
The population of a town increased by 80 % in 5 years. If the population is currently 40,000 , find the population of this town 5 years ago. (Round to the nearest whole, if necessary.)

A) 8000
B) 50,000
C) 32,000
D) 22,222

Question 72

Solve.
A car rental agency adverised renting a luxury, full-size car for $29.95 per day and $0.29 per mile. If you rent this car for 4 days, how many whole miles can you drive if you only have $200 to spens.

A) 50
B) 572
C) 276
D) 21

Question 73

Solve.
The sum of three consecutive even integers is 318 . Find the integers.

A) 105,106,107
B) 104,106,108
C) 106,108,110
D) 102,104,106

Question 74

Solve.
A 9-ft. board is cut into 2 pieces so that one piece is 5 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

A) shorter piece: 1 ft .; longer piece: 8 ft
B) shorter piece: 22 ft ; longer piece: 27 ft .
C) shorter piece: 4.5 ft ; longer piece: 27 ft .
D) shorter piece: 15 ft ; longer piece: 32 ft .

Question 75

Solve the equation for the specified variable.
V= lwh for w

A) $w = \frac { V l } { h }$
B) $\mathrm { w } = \frac { \mathrm { Vh } } { \mathrm { l } }$
C) w=Vlh
D) $w = \frac { V } { l h }$

Question 76

Solve.
The cost C to product x number of tennis rackets is C=190 +18x. The tennis rackets are sold wholesale for $23 each, so revenue R =23x. Find how many tennis rackets the manufacturer needs to produce and sell to break even.

A) 43 tennis rackets
B) 33 tennis rackets
C) 19 tennis rackets
D) 38 tennis rackets

Question 77

Solve the equation for the specified variable.
$\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ for h

A) $h = \frac { b } { 2 A }$
B) $h = \frac { A b } { 2 }$
C) $h = \frac { A } { 2 b }$
D) $h = \frac { 2 \mathrm {~A} } { \mathrm {~b} }$

Question 78

Solve.
A diamond ring sold for $2570.40 including tax. If the tax rate where the diamond was purchased is 7.1%, Find the price of the ring befor the tax was added. (Round to the nearest cent, if necessary.)

A) $182.50
B) $2752.90
C) $2400.00
D) $2387.90

Question 79

Solve.
Seven times some number added to 8 amounts to -10 added to the product of 4 and the number.

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

Question 80

Solve.
A publisher printed 84 million pages in its production process last year. If this represents a 120 % increase over the number of pages printed the previous year, how many pages were printed the previous year? (Round to the nearest hundredth million, if necessary.)

A) 14,400 million pages
B) 700 million pages
C) 70 million pages
D) 144 million pages