Question 1

Solve using the addition principle.
-15 = -14 + a
A)-1
B)1
C)-29
D)29

Accepted Answer

To solve for variable a, we need to isolate it on one side of the equation. Using the addition principle, we can add 14 to both sides:

15 + 14 = -14 + 14 + a

29 = a

Therefore, the solution is a = 29. Choice D is the correct answer.

Question 2

Determine whether it is true or false that the given number is a solution of the equation.
--14; 8(y - 4)= 144

Accepted Answer

Substituting -14 for y in the equation 8(y - 4) = 144 gives 8(-14 - 4) = 8(-18), which does not equal 144.

Question 3

Determine whether it is true or false that the given number is a solution of the equation.
--7; 8x = -56.

Accepted Answer

To check if -7 is a solution of the equation, we can substitute -7 for x and see if the equation is true:

8(-7) = -56

-56 = -56

Since the equation is true when x is -7, -7 is a solution of the equation. To check if -7 is a solution of the equation, we substitute it for x and simplify:
8x = -56
8(-7) = -56
-56 = -56

Since the equation is true with x = -7, we can say that -7 is a solution of the equation. Therefore, the answer is A.

Question 4

Determine whether it is true or false that the given number is a solution of the equation.
--3; 3x = -12.

Accepted Answer

The answer of Determine whether it is true or false...

Question 5

Solve using the addition principle.
-
A) 
B) 
C)1
D)

Accepted Answer

The answer of Solve using the addition principle.
-
A) 
B) 
C)1
D)...

Question 6

Solve using the addition principle.
--27 = y - 52
A)25
B)-25
C)79
D)-79

Accepted Answer

The answer of Solve using the addition principle.
--27 = y...

Question 7

Solve using the addition principle.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve using the addition principle.
-
A) 
B) 
C)...

Question 8

Solve using the addition principle.
-s - 7 = 13
A)6
B)-20
C)20
D)-6

Accepted Answer

To solve using the addition principle, we want to isolate the variable (s) on one side of the equation by adding the same number to both sides. 
s - 7 + 7 = 13 + 7 
s = 20 
Therefore, the answer is C)20. To solve using the addition principle, we need to isolate the variable s on one side of the equation by adding 7 to both sides:

s - 7 + 7 = 13 + 7

s = 20

Therefore, the answer is choice C, which is 20.

Question 9

Determine whether it is true or false that the given number is a solution of the equation.
--5; 8x - 4x = -64.

Accepted Answer

To check whether a number is a solution of an equation, we substitute the given number in place of the variable(s) and simplify both sides. If the resulting equation is true, then the given number is a solution. If the resulting equation is false, then the given number is not a solution.

In this case, we are asked to check whether -5 is a solution of the equation 8x - 4x = -64. Substituting -5 for x, we get:

8(-5) - 4(-5) = -64
-40 + 20 = -64
-20 = -64

The resulting equation is false, since -20 does not equal -64. Therefore, -5 is not a solution of the equation. The answer is B, False.

Question 10

Solve using the addition principle.
-x + 3 = 9
A)-12
B)6
C)-6
D)12

Accepted Answer

To solve for x, we need to isolate it on one side of the equation. Using the addition principle, we can subtract 3 from both sides of the equation: 
x + 3 - 3 = 9 - 3 
x = 6 
Therefore, the solution is x = 6, which corresponds to choice B. To solve using the addition principle, we want to isolate the variable on one side of the equation. To do this, we will subtract 3 from both sides:

x + 3 - 3 = 9 - 3

Simplifying:

x = 6

Therefore, the answer is choice B, 6.

Question 11

Determine whether it is true or false that the given number is a solution of the equation.
--4; 7x - 2 = -30.

Accepted Answer

To check if -4 is a solution of the equation, we substitute it for x in the equation and check if the equation is true:

7(-4) - 2 = -30

-28 - 2 = -30

-30 = -30

Since the equation is true, -4 is a solution of the equation. Substitute -4 for x in the equation:
7(-4) - 2 = -30
-28 - 2 = -30
-30 = -30
Since the equation is true, -4 is a solution of the equation.

Question 12

Determine whether it is true or false that the given number is a solution of the equation.
-

Accepted Answer

The answer of Determine whether it is true or false...

Question 13

Solve using the addition principle.
-z - 4.87 = -12.8
A)-17.67
B)7.93
C)-7.93
D)17.67

Accepted Answer

The answer of Solve using the addition principle.
-z - 4.87...

Question 14

Solve using the addition principle.
--24.8 - x = 29.3
A)-4.5
B)4.5
C)54.1
D)-54.1

Accepted Answer

The answer of Solve using the addition principle.
--24.8 - x...

Question 15

Solve using the multiplication principle.
-5x = 50
A)45
B)10
C)250
D)

Accepted Answer

To solve for x, we need to isolate it on one side of the equation. Since 5x = 50, we can divide both sides by 5 to get x = 10. Therefore, the answer is B, 10. To solve for x, we need to isolate it on one side of the equation. Since 5x = 50, we can divide both sides by 5 to get x = 10. Therefore, the correct choice is B, which represents the value of x that satisfies the equation.

Question 16

Determine whether it is true or false that the given number is a solution of the equation.
--8; 6x + 3x = -72.

Accepted Answer

To check if -8 is a solution to the equation, we replace x with -8 and simplify:
6x + 3x = -72
6(-8) + 3(-8) = -72
-48 - 24 = -72
-72 = -72
Since the equation is true when x = -8, -8 is indeed a solution to the equation. Therefore, the answer is A)True. Substituting -8 for x in the equation gives:

6(-8) + 3(-8) = -72

-48 - 24 = -72

-72 = -72

Therefore, -8 is a solution to the equation.

Question 17

Determine whether it is true or false that the given number is a solution of the equation.
-

Accepted Answer

The answer of Determine whether it is true or false...

Question 18

Determine whether it is true or false that the given number is a solution of the equation.
-20; 7(y - 7)= 91

Accepted Answer

Substitute y = 20 into the equation:
7(y - 7) = 91
7(20 - 7) = 91
7(13) = 91
91 = 91
Since the equation is true, y = 20 is a solution. Substituting 20 for y in the equation 7(y - 7)= 91, we get:
7(20-7) = 7(13) = 91
Since this is the same as the right-hand side of the equation, 20 is a solution to the equation.

Question 19

Solve using the addition principle.
--27 + z = -81
A)108
B)54
C)-54
D)-108

Accepted Answer

To solve the equation -27 + z = -81 for z, you add 27 to both sides of the equation to isolate z, resulting in z = -81 + 27, which simplifies to z = -54.

Question 20

Determine whether it is true or false that the given number is a solution of the equation.
-6; -7x + 3 = -44.

Accepted Answer

When you substitute 6 for x in the equation -7x + 3 = -44, you get -7(6) + 3 = -42 + 3 = -39, which is not equal to -44.

Quiz 1: Solving Linear Equations and Inequalities

Solve using the addition principle. -15 = -14 + a

Determine whether it is true or false that the given number is a solution of the equation. --14; 8(y - 4)= 144

Determine whether it is true or false that the given number is a solution of the equation. --7; 8x = -56.

Determine whether it is true or false that the given number is a solution of the equation. --3; 3x = -12.

Solve using the addition principle. -

Solve using the addition principle. --27 = y - 52

Solve using the addition principle. -

Solve using the addition principle. -s - 7 = 13

Determine whether it is true or false that the given number is a solution of the equation. --5; 8x - 4x = -64.

Solve using the addition principle. -x + 3 = 9

Determine whether it is true or false that the given number is a solution of the equation. --4; 7x - 2 = -30.

Determine whether it is true or false that the given number is a solution of the equation. -

Solve using the addition principle. -z - 4.87 = -12.8

Solve using the addition principle. --24.8 - x = 29.3

Solve using the multiplication principle. -5x = 50

Determine whether it is true or false that the given number is a solution of the equation. --8; 6x + 3x = -72.

Determine whether it is true or false that the given number is a solution of the equation. -

Determine whether it is true or false that the given number is a solution of the equation. -20; 7(y - 7)= 91

Solve using the addition principle. --27 + z = -81

Determine whether it is true or false that the given number is a solution of the equation. -6; -7x + 3 = -44.