Question 1

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) $\left\{ - \frac { 5 } { 3 } \right\}$

Accepted Answer

Combining like terms on the left side gives $3x - 3 = -2x$. Adding $2x$ to both sides results in $5x - 3 = 0$. Adding $3$ to both sides gives $5x = 3$. Dividing both sides by $5$ results in $x = \frac{3}{5}$.

Question 2

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) $\{ - 8 \}$

Accepted Answer

To solve $5x - 8 = 56 - 3x$, first add $3x$ to both sides to get $8x - 8 = 56$. Then add $8$ to both sides to get $8x = 64$. Finally, divide both sides by $8$ to find $x = 8$.

Question 3

Solve the equation using both the addition and multiplication properties of equality.
--4x = 66 + 7x
A) {6}
B) {77}
C) {-5}
D) {-6}

Accepted Answer

To solve the equation -4x = 66 + 7x, first combine like terms by getting all x terms on one side. Add 4x to both sides to get 0 = 66 + 11x. Then, subtract 66 from both sides to get 11x = -66. Finally, divide both sides by 11 to find x = -6.

Question 4

Solve the equation using both the addition and multiplication properties of equality.
--3 = -3x + 6
A) {-3}
B) {10}
C) {6}
D) {3}

Accepted Answer

First, subtract 6 from both sides to get -9 = -3x. Then, divide both sides by -3 to solve for x, resulting in x = 3.

Question 5

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

Accepted Answer

Using the formula $ \mathrm{W} = \mathrm{P} \times \mathrm{t} $, we calculate work as $ 800 \, \text{watts} \times 27 \, \text{seconds} = 21,600 \, \text{joules} $.

Question 6

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) $\left\{ - \frac { 7 } { 3 } \right\}$

Accepted Answer

To solve the equation $10y - 35 = 5y$, first subtract $5y$ from both sides to get $5y - 35 = 0$. Then add $35$ to both sides to get $5y = 35$. Finally, divide both sides by $5$ to find $y = 7$, which corresponds to choice B.

Question 7

Solve the equation using both the addition and multiplication properties of equality.
-12x - 7 = 4x + 17
A) {6}
B) {1}
C) {3}
D) {4}

Accepted Answer

The answer of Solve the equation using both the addition...

Question 8

Solve the equation using both the addition and multiplication properties of equality.
-5n - 8 = 37
A) {9}
B) {44}
C) {40}
D) {15}

Accepted Answer

First, add 8 to both sides of the equation to get 5n = 45. Then, divide both sides by 5 to solve for n, which gives n = 9.

Question 9

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) $\frac { 3 } { 4 } + x = 6 ; \frac { 21 } { 4 }$

Accepted Answer

The correct equation that represents the given information is $\frac{3}{4}x = 6$. Solving this equation for $x$ gives $x = 8$.

Question 10

Solve the equation.
--x = -14
A) {0}
B) {-14}
C) {-1}
D) {14}

Accepted Answer

To solve the equation -x = -14, you would multiply both sides by -1 to get x = 14. Therefore, the solution is {14}.

Question 11

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

Accepted Answer

The correct equation that represents "a number subtracted from eighteen is four" is 18 - x = 4. Solving this equation for x gives x = 14.

Question 12

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

Accepted Answer

The formula to find the distance is $d = t \times r$. Given $t = 30$ minutes and $r = 0.7$ mile per minute, the distance $d = 30 \times 0.7 = 21$ miles.

Question 13

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

Accepted Answer

Using the formula $t = \frac{d}{r}$, we can rearrange it to solve for distance $d = t \times r$. Substituting $t = 4$ hours and $r = 60$ miles per hour, we get $d = 4 \times 60 = 240$ miles.

Question 14

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) $\{ 3 \}$

Accepted Answer

The answer of Solve the equation using both the addition...

Question 15

Solve the equation using both the addition and multiplication properties of equality.
-8r + 10 = 34
A) {20}
B) {5}
C) {16}
D) {3}

Accepted Answer

The answer of Solve the equation using both the addition...

Question 16

Solve the equation using both the addition and multiplication properties of equality.
--2x - 25 = -57
A) 41
B) {-30}
C) {-16}
D) {16}

Accepted Answer

The answer of Solve the equation using both the addition...

Question 17

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

Accepted Answer

The answer of Solve the problem.
-To convert meters to feet,...

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 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) $\frac { x } { 30 } = 5 ; 150$

Accepted Answer

The correct equation that represents the given situation is $\frac { 30 } { x } = 5$. Solving this equation for $x$ gives $x = 6$.

Question 19

Solve the equation using both the addition and multiplication properties of equality.
--13 = 7x + 1
A) {-21}
B) {-2}
C) {-17}
D) {2}

Accepted Answer

First, subtract 1 from both sides to get -14 = 7x. Then, divide both sides by 7 to solve for x, resulting in x = -2.

Question 20

Solve the equation using both the addition and multiplication properties of equality.
--12 = -2x + 8
A) {-18}
B) {2}
C) {10}
D) {-14}

Accepted Answer

First, subtract 8 from both sides to get -20 = -2x. Then, divide both sides by -2 to solve for x, resulting in x = 10.

Quiz 2: Linear Equations and Inequalities in One Variable

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

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

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

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

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

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

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

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.

Solve the equation. --x = -14

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.

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?

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?

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

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

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

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?

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.

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

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

Quiz 2: Linear Equations and Inequalities in One Variable

Solve the equation using both the addition and multiplication properties of equality. - 6x−3x−3=−2x6 x - 3 x - 3 = - 2 x6x−3x−3=−2x

Solve the equation using both the addition and multiplication properties of equality. - 5x−8=56−3x5 x - 8 = 56 - 3 x5x−8=56−3x

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

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

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

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

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

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.

Solve the equation. --x = -14

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.

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?

Solve the problem. -The time it takes to travel a given distance at constant speed is given by the formula t =dr= \frac { \mathrm { d } } { \mathrm { r } }=rd​ 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?

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

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

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

Solve the problem. -To convert meters to feet, you can use the formula f f=m0.3038\mathrm { f } = \frac { \mathrm { m } } { 0.3038 }f=0.3038m​ , where f is the distance in feet and m is the distance in meters. How many meters (to the nearest tenth) is 24 feet?

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.

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

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

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

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

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?

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?