Question 1

Let x represent the number. Write the English phrase as an algebraic expression.
-The product of 6 and a number, added to 14.

Accepted Answer

A)  6 + 14x 
B)  14 + 6x 
C)  84 + x 
D)  84x 
A)  6 + 14x 
B)  14 + 6x 
C)  84 + x 
D)  84x

Question 2

Solve the equation.
-$$- 7 ( x + 2 ) = - 49$$

Accepted Answer

A)  $\{ - 47 \}$ 
B)  $\{ - 51 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ - 47 \}$ 
B)  $\{ - 51 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 5 \}$

Question 3

Let x represent the number. Write the English phrase as an algebraic expression.
-Eleven times a number decreased by one-third of the same number.

Accepted Answer

A)  $11 x - \frac { 1 } { 3 }$ 
B)  $11 x - \frac { x } { 3 }$ 
C)  $11 \left( x - \frac { 1 } { 3 } \right)$ 
D)  $\frac { x } { 3 } - 11 x$ 
A)  $11 x - \frac { 1 } { 3 }$ 
B)  $11 x - \frac { x } { 3 }$ 
C)  $11 \left( x - \frac { 1 } { 3 } \right)$ 
D)  $\frac { x } { 3 } - 11 x$

Question 4

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.

Accepted Answer

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

Question 5

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?

Accepted Answer

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

Question 6

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

Accepted Answer

A)  linear 
B)  not linear 
A)  linear 
B)  not linear

Question 7

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

Accepted Answer

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

Question 8

Let x represent the number. Write the English phrase as an algebraic expression.
-The quotient of 31 and the product of a number and $- 10$.

Accepted Answer

A)  $\frac { 31 } { x } - 10$ 
B)  $- 310 x$ 
C)  $\frac { 31 } { - 10 x }$ 
D)  $\frac { - 10 \mathrm { x } } { 31 }$ 
A)  $\frac { 31 } { x } - 10$ 
B)  $- 310 x$ 
C)  $\frac { 31 } { - 10 x }$ 
D)  $\frac { - 10 \mathrm { x } } { 31 }$

Question 9

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

Accepted Answer

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

Question 10

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all
real numbers.
-$$6 ( x + 6 ) + 44 = 8 x - 2 ( x + 8 )$$

Accepted Answer

A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\{ 60 \}$ 
C)  $\varnothing$ 
D)  $\{ 28 \}$ 
A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\{ 60 \}$ 
C)  $\varnothing$ 
D)  $\{ 28 \}$

Question 11

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

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\{ 20 \}$ 
C)  $\{ 10 \}$ 
D)  $\{ 40 \}$ 
A)  $\{ 8 \}$ 
B)  $\{ 20 \}$ 
C)  $\{ 10 \}$ 
D)  $\{ 40 \}$

Question 12

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-The sum of four times a number and 6 is equal to the difference of twice the number and 10. Find the number.

Accepted Answer

A)  $4 x + 6 = 2 x - 10 ; 8$ 
B)  $4 x + 6 = 2 x - 10 ; - 8$ 
C)  $4 ( x + 6 ) = 2 x - 10 ; - 17$ 
D)  $4 x + 6 = 2 x + 10 ; 2$ 
A)  $4 x + 6 = 2 x - 10 ; 8$ 
B)  $4 x + 6 = 2 x - 10 ; - 8$ 
C)  $4 ( x + 6 ) = 2 x - 10 ; - 17$ 
D)  $4 x + 6 = 2 x + 10 ; 2$

Question 13

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
-Three-fourths of a number is 56 . Find the number in lowest terms.

Accepted Answer

A)  $\frac { 3 } { 4 } x = \frac { 5 } { 6 } ; \frac { 5 } { 8 }$ 
B)  $\frac { 3 } { 4 } + x = \frac { 5 } { 6 } ; \frac { 1 } { 10 }$ 
C)  $\frac { 3 } { 4 } x = \frac { 5 } { 6 } ; \frac { 10 } { 9 }$ 
D)  $\frac { 3 } { 4 } x = \frac { 5 } { 6 } ; \frac { 20 } { 18 }$ 
A)  $\frac { 3 } { 4 } x = \frac { 5 } { 6 } ; \frac { 5 } { 8 }$ 
B)  $\frac { 3 } { 4 } + x = \frac { 5 } { 6 } ; \frac { 1 } { 10 }$ 
C)  $\frac { 3 } { 4 } x = \frac { 5 } { 6 } ; \frac { 10 } { 9 }$ 
D)  $\frac { 3 } { 4 } x = \frac { 5 } { 6 } ; \frac { 20 } { 18 }$

Question 14

Solve the equation.
-4(5x + 1) + 23 = 14x - 3

Accepted Answer

A)  {-30} 
B)  {-180} 
C)  {-5} 
D)  {5} 
A)  {-30} 
B)  {-180} 
C)  {-5} 
D)  {5}

Question 15

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

Accepted Answer

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

Question 16

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?

Accepted Answer

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

Question 17

Solve the problem.
-If 100 is decreased to 95, the decrease is what percent of the original number?

Accepted Answer

A)  5% 
B)  0.5% 
C)  0.0005% 
D)  0.05% 
A)  5% 
B)  0.5% 
C)  0.0005% 
D)  0.05%

Question 18

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.

Accepted Answer

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

Question 19

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.

Accepted Answer

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

Question 20

Solve the equation.
-$$2 x + 3 ( - 2 x - 4 ) = - 7 - 9 x$$

Accepted Answer

A)  $\left\{ \frac { 19 } { 13 } \right\}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ - \frac { 19 } { 5 } \right\}$ 
D)  $\{ 1 \}$ 
A)  $\left\{ \frac { 19 } { 13 } \right\}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ - \frac { 19 } { 5 } \right\}$ 
D)  $\{ 1 \}$

Let x represent the number. Write the English phrase as an algebraic expression. -The product of 6 and a number, added to 14.

Solve the equation. - $- 7 ( x + 2 ) = - 49$

Let x represent the number. Write the English phrase as an algebraic expression. -Eleven times a number decreased by one-third of the same number.

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.

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?

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

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

Let x represent the number. Write the English phrase as an algebraic expression. -The quotient of 31 and the product of a number and $- 10$ .

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

Solve the equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. - $6 ( x + 6 ) + 44 = 8 x - 2 ( x + 8 )$

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

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -The sum of four times a number and 6 is equal to the difference of twice the number and 10. Find the number.

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. -Three-fourths of a number is 56 . Find the number in lowest terms.

Solve the equation. -4(5x + 1) + 23 = 14x - 3

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

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?

Solve the problem. -If 100 is decreased to 95, the decrease is what percent of the original number?

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.

Solve the equation. - $2 x + 3 ( - 2 x - 4 ) = - 7 - 9 x$

Variables, Real Numbers, and Mathematical Models

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Basics of Functions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 2: Linear Equations and Inequalities in One Variable