Master Equation Solving: A Comprehensive Guide for Year 8 Maths

Question 1

In the equation 2x - 5 = 11, what is the value of x?

Accepted Answer

4

Answer

3

Answer

8

Answer

16

Question 2

If the sum of two numbers is 25 and one number is x, what is the other number?

Accepted Answer

25 - x

Answer

x - 25

Answer

x + 25

Answer

x / 25

Question 3

Which of these is a two-step equation?

Accepted Answer

3(x + 2) = 15

Answer

x + 5 = 10

Answer

2x - 5 = 11

Answer

x^2 = 25

Question 4

Solve the equation: 2(x - 3) = 8

Accepted Answer

x = 6

Answer

x = 2

Answer

x = 4

Answer

x = 8

Question 5

Find the value of m in the equation: 3m - 5 = 2m + 10

Accepted Answer

m = 5

Answer

m = -5

Answer

m = 15

Answer

m = -15

Question 6

Which of the following equations has no solution? Select the equation with no solution.

Accepted Answer

x^2 = -9

Answer

x + 5 = x - 3

Answer

2x + 1 = x + 4

Answer

3x - 5 = 2x - 7

Question 7

Which of the following is a linear equation? Select the linear equation.

Accepted Answer

y = 2x - 3

Answer

y = x^2 + 1

Answer

y = |x|

Answer

y = sin(x)

Question 8

Which of the following is an equation?

Accepted Answer

x equals 5

Answer

x plus 5

Answer

x minus 5

Answer

5 multiplied by x

Question 9

Which of the following is the opposite operation of multiplying?

Accepted Answer

Dividing

Answer

Adding

Answer

Subtracting

Answer

Raising to a power

Question 10

Which of the following is a variable?

Accepted Answer

x

Answer

5

Answer

10

Answer

+

Question 11

What is the coefficient of x in the expression 4x minus 7?

Accepted Answer

4

Answer

7

Answer

x

Answer

-7

Question 12

Translate the following phrase into an algebraic equation: 'A number increased by six is equal to ten'

Accepted Answer

x + 6 = 10

Answer

6 + x = 10

Answer

10 - x = 6

Answer

10 + x = 6

Question 13

The total of two numbers is 25. If we represent one number as x, what is the other number?

Accepted Answer

25 - x

Answer

x + 25

Answer

25 - 2x

Answer

x - 25

Question 14

Which of the following is NOT a valid equation?

Accepted Answer

x - 2 > 10

Answer

x = 5

Answer

5 = x

Answer

x + x = 2

Question 15

The equation x - 3 = 7 is equivalent to:

Accepted Answer

x = 4

Answer

x = 10

Answer

x = -4

Answer

x = 14

Question 16

Which method would be most suitable to verify if x = 5 is a solution to the equation 3(x - 2) = 15?

Accepted Answer

Substitute x = 5 into the equation

Answer

Solve the equation for x

Answer

Graph the equation

Answer

Factor the equation

Question 17

Solve for x in 2x - 5 = 15.

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 18

Solve for x: x + 5 = 12

Accepted Answer

7

Answer

5

Answer

12

Answer

17

Question 19

Solve for w: 10 ÷ w = 5

Accepted Answer

0.5

Answer

2

Answer

5

Answer

10

Question 20

Which of the following is an equivalent equation to 3x - 2 = 10?

Accepted Answer

3x = 8

Answer

x - 2 = 10

Answer

x + 2 = 13

Answer

x = 4

Question 21

Solve for y: y - 7 = 3

Accepted Answer

y = 4

Answer

y = 10

Answer

y = 14

Answer

y = 21

Question 22

Solve for x: 2x = 12

Accepted Answer

x = 4

Answer

x = 6

Answer

x = 8

Answer

x = 10

Question 23

Find the value of x in the equation 2(x - 4) = 10

Accepted Answer

x = 7

Answer

x = 3

Answer

x = 9

Answer

x = 11

Question 24

Which of the following equations has the solution x = -2?

Accepted Answer

x - 3 = -5

Answer

x + 3 = 5

Answer

2x = -4

Answer

3x = 6

Question 25

Which of the choices is NOT an equation?

Accepted Answer

x = 5

Answer

5 + x = 12

Answer

x - 3 = 7

Answer

2x + 1 = 9

Question 26

Solve the equation: x + 5 = 10

Accepted Answer

x = 5

Answer

x = 10

Answer

x = 15

Answer

x = 20

Question 27

Which equation has a solution of x = 3?

Accepted Answer

2x - 6 = 0

Answer

x - 5 = 8

Answer

3x + 1 = 10

Answer

x + 5 = 11

Question 28

Which of the choices is a quadratic equation?

Accepted Answer

x^2 + 2x + 1 = 0

Answer

x + 5 = 10

Answer

3x - 6 = 12

Answer

x / 4 = 5

Question 29

Find the value of x in the equation: x + 5 = 12

Accepted Answer

7

Answer

5

Answer

12

Answer

17

Question 30

Which of the following is not an equation?

Accepted Answer

5 > x + 2

Answer

x + 5 = 12

Answer

y = 3

Answer

x + 1 = x

Question 31

Solve the equation for x: 2x^2 - 5x + 2 = 0

Accepted Answer

x = 1 or x = 2

Answer

x = -1 or x = -2

Answer

x = 1/2 or x = 1

Answer

x = -1/2 or x = -1

Question 32

Which of the following is a linear equation?

Accepted Answer

y = 3x + 2

Answer

y = x^2

Answer

y = 1/x

Answer

y = sqrt(x)

Question 33

Solve the inequality: 2x - 5 > 11

Accepted Answer

x > 4

Answer

x > 8

Answer

x < 4

Answer

x < 8

Question 34

Which of the following equations has the solution x = 0?

Accepted Answer

4x = 0

Answer

2x + 5 = 10

Answer

3x - 4 = -4

Answer

x + 2 = 2

Question 35

Solve the system of equations:
    x + y = 5
    x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Answer

The system has no solutions

Question 36

Which of the following is equivalent to the expression 2(x - 3)?

Accepted Answer

2x - 6

Answer

2x - 3

Answer

x - 6

Answer

4x - 3

Question 37

Which of the following statements is NOT an equation?

Accepted Answer

The sum of two numbers is 10

Answer

4x = 20

Answer

2 + 3 = 5

Answer

x^2 = 4

Question 38

Find the solution to the equation: x + 5 = 12

Accepted Answer

x = 7

Answer

x = 5

Answer

x = 17

Answer

x = 2

Question 39

Translate the situation into an equation: A number decreased by 6 is equal to 10?

Accepted Answer

x - 6 = 10

Answer

x + 6 = 10

Answer

6 - x = 10

Answer

10 - x = 6

Question 40

Translate the situation into an equation: Twice a number added to 5 is equal to 15?

Accepted Answer

2x + 5 = 15

Answer

x + 2 = 15

Answer

x - 5 = 15

Answer

2x - 5 = 15

Question 41

Translate the following statement into an algebraic equation: 'The total of a number x and five is equal to twelve'.

Accepted Answer

x + 5 = 12

Answer

12 - x = 5

Answer

12 + x = 5

Answer

x - 5 = 12

Question 42

Solve for y in the equation: 3(y - 2) + 5 = 14

Accepted Answer

3

Answer

4

Answer

2

Question 43

The length of a rectangle is represented by x. Its width is three more than its length. Write an algebraic expression for the area of the rectangle.

Accepted Answer

x(x + 3)

Answer

(x + 3)²

Answer

(x + 3) - x

Answer

x + (x + 3)

Question 44

Which equation represents the statement '5 less than twice a number is 11'?

Accepted Answer

2x - 5 = 11

Answer

5 - 2x = 11

Answer

5x - 2 = 11

Answer

2x + 5 = 11

Question 45

Solve for 'y':  y - 7 = 12

Accepted Answer

y = 19

Answer

y = -5

Answer

y = 5

Answer

y = -19

Question 46

Solve for 'm':  m / 4 = 8

Accepted Answer

m = 32

Answer

m = 2

Answer

m = 4

Answer

m = 12

Question 47

Which of the following is NOT an equation?

Accepted Answer

5x + 2

Answer

3y = 15

Answer

4z + 1 = 9

Answer

2x - 7 = 11

Question 48

The perimeter of a rectangle is 24 cm. If the length is 'l' and the width is 'w', which equation represents this information?

Accepted Answer

2l + 2w = 24

Answer

l * w = 24

Answer

l + w = 24

Answer

l - w = 24