Question 1

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all
real numbers.
-$$7 ( x + 5 ) = 7 x - 70$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 70 \}$ 
C)  $\{ x \mid x$ is a real number $\}$ 
D)  $\{ 0 \}$

Question 2

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.

Accepted Answer

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

Question 3

Solve the equation.
-1.6 - 9.5x = -48.2 - 1.2x

Accepted Answer

A)  {5.4} 
B)  {-58} 
C)  {5.2} 
D)  {6}

Question 4

Solve the equation.
-$2.1 + x = 17.6$

Accepted Answer

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

Question 5

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-Rooms in Dormitory A each have 132 square feet of floor space. These rooms have twice as much floor space as each room in Dormitory B. About how much floor space does a room in Dormitory B have?

Accepted Answer

A)  130 sq. feet 
B)  264 sq. feet 
C)  134 sq. feet 
D)  66 sq. feet

Question 6

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $73 under this promotional deal, how many minutes of phone calls did he make? Round to
The nearest integer, if necessary.

Accepted Answer

A)  3 minutes 
B)  1760 minutes 
C)  1160 minutes 
D)  12 minutes

Question 7

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

Accepted Answer

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

Question 8

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?

Accepted Answer

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

Question 9

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all
real numbers.
-$$9 x + 8 + 5 x + 5 = 5 x + 9 x + 10$$

Accepted Answer

A)  $\{ 160 \}$ 
B)  $\{ 0 \}$ 
C)  $\varnothing$ 
D)  $\{ x \mid x$ is a real number $\}$

Question 10

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

Accepted Answer

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

Question 11

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all
real numbers.
-$$- 8 x + 6 + 6 x = - 2 x + 11$$

Accepted Answer

A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\varnothing$ 
C)  $\{ 5 \}$ 
D)  $\{ - 6 \}$

Question 12

Use a formula for perimeter or area to solve the problem.
-The length of a rectangle is 121 in. and the width is 33 in. Find its perimeter.

Accepted Answer

A)  308 in. 
B)  3993 in. 
C)  154 in. 
D)  275 in.

Question 13

Use a formula for perimeter or area to solve the problem.
-
Find the area of the triangle.

Accepted Answer

A)  $120 \mathrm {~km} ^ { 2 }$ 
B)  $68 \mathrm {~km} ^ { 2 }$ 
C)  $60 \mathrm {~km} ^ { 2 }$ 
D)  $40 \mathrm {~km} ^ { 2 }$

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all
real numbers.
-$$9 x + 1 = 1 - x$$

Accepted Answer

A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\left\{ \frac { 9 } { 2 } \right\}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$

Question 17

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all
real numbers.
-15% of students at a university attended a lecture. If 4000 students are enrolled at the university, about how many students attended the lecture?

Accepted Answer

A)  60,000 students 
B)  6000 students 
C)  60 students 
D)  600 students

Question 18

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

Accepted Answer

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 19

Let x represent the number. Write the English phrase as an algebraic expression.
-Five times a number, decreased by 19.

Accepted Answer

A)  5(x + 19) 
B)  5x - 19 
C)  5(x - 19) 
D)  5x + 19

Question 20

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

Accepted Answer

A)  {-29} 
B)  {29} 
C)  {11} 
D)  {-11}

Exam 2: Linear Equations and Inequalities in One Variable

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - $7 ( x + 5 ) = 7 x - 70$

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.

Solve the equation. -1.6 - 9.5x = -48.2 - 1.2x

Solve the equation. - $2.1 + x = 17.6$

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

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - $9 x + 8 + 5 x + 5 = 5 x + 9 x + 10$

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

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - $- 8 x + 6 + 6 x = - 2 x + 11$

Use a formula for perimeter or area to solve the problem. -The length of a rectangle is 121 in. and the width is 33 in. Find its perimeter.

Use a formula for perimeter or area to solve the problem. - $Use a formula for perimeter or area to solve the problem. - Find the area of the triangle. A) 120 \mathrm {~km} ^ { 2 } B) 68 \mathrm {~km} ^ { 2 } C) 60 \mathrm {~km} ^ { 2 } D) 40 \mathrm {~km} ^ { 2 }$ Find the area of the triangle.

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

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

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - $9 x + 1 = 1 - x$

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. -15% of students at a university attended a lecture. If 4000 students are enrolled at the university, about how many students attended the lecture?

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

Let x represent the number. Write the English phrase as an algebraic expression. -Five times a number, decreased by 19.

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

Exam 2: Linear Equations and Inequalities in One Variable

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - 7(x+5) =7x−707 ( x + 5 ) = 7 x - 707(x+5) =7x−70

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.

Solve the equation. -1.6 - 9.5x = -48.2 - 1.2x

Solve the equation. - 2.1+x=17.62.1 + x = 17.62.1+x=17.6

Solve the equation. - 14x−9=6x+1514 x - 9 = 6 x + 1514x−9=6x+15

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - 9x+8+5x+5=5x+9x+109 x + 8 + 5 x + 5 = 5 x + 9 x + 109x+8+5x+5=5x+9x+10

Solve the equation. - x+16=56x + \frac { 1 } { 6 } = \frac { 5 } { 6 }x+61​=65​

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - −8x+6+6x=−2x+11- 8 x + 6 + 6 x = - 2 x + 11−8x+6+6x=−2x+11