Chapter 10 · Class 8 CBSE · MCQ Test
Linear Equations MCQ Test — Class 8 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Linear Equations — MCQ Questions
1Which of the following expressions is NOT a linear equation in one variable?
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Answer: p² - 4 = 0
Hint: Recall the definition of a linear equation: the highest power of the variable must be 1.
Solution:
A linear equation in one variable is an equation where the highest power of the variable is 1.
In options A, B, and C, the variables x, y, and z all have a power of 1.
In option D, the variable 'p' has a power of 2 (p²), making it a quadratic equation, not a linear equation.
2Ravi was solving the equation 5x + 3 = 2x - 6. His first step was 5x - 2x = -6 + 3. What mistake did he make?
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Answer: When transposing +3 to the right side, it should become -3.
Hint: Remember the rule for transposing terms from one side of an equation to the other.
Solution:
When a term is transposed from one side of the equation to the other, its sign changes.
Ravi correctly transposed 2x from the right side to the left side (2x became -2x).
However, when transposing +3 from the left side to the right side, it should become -3, not +3.
The correct first step after transposing would be 5x - 2x = -6 - 3.
3If 7 is added to five times a number, the result is the same as 10 added to three times the same number. What is the number?
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Answer: 3/2
Hint: Formulate the equation by representing the unknown number as a variable, say 'x', and then set up the equality based on the given conditions.
Solution:
Let the number be 'x'.
Five times the number with 7 added: 5x + 7.
Three times the number with 10 added: 3x + 10.
Set them equal: 5x + 7 = 3x + 10.
Solve for x: 5x - 3x = 10 - 7 => 2x = 3 => x = 3/2.
4Which of the following statements is TRUE about linear equations?
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Answer: Dividing both sides of an equation by the same non-zero number maintains the equality.
Hint: Think about the fundamental properties of equality that allow us to manipulate equations without changing their solution.
Solution:
Option A is false: Adding a number to only one side changes the equality.
Option B is false: Multiplying both sides by zero makes both sides zero, which changes the original equation and its solution (e.g., 2x=4 becomes 0=0).
Option C is true: This is a fundamental property of equality, allowing us to simplify equations. The number must be non-zero to avoid division by zero.
Option D is false: To maintain equality, the *same* number must be subtracted from both sides.
5Solve for x: 3(x - 2) + 5 = 2x - 1
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Answer: x = 0
Hint: First, distribute the number outside the bracket on the left side, then simplify and gather like terms.
Solution:
Expand the bracket: 3x - 6 + 5 = 2x - 1.
Combine constants on the left side: 3x - 1 = 2x - 1.
Transpose terms: 3x - 2x = -1 + 1.
Simplify: x = 0.
6If x = -4 is the solution to an equation, which of the following equations is NOT satisfied by x = -4?
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Answer: x/2 - 1 = x - 1
Hint: Substitute x = -4 into each equation and check which one results in a false statement (left side not equal to right side).
Solution:
Substitute x = -4 into each equation:
A) 3(-4) + 1 = -11; (-4) - 7 = -11. (True)
B) 2(-4 + 5) = 2(1) = 2; (-4) + 6 = 2. (True)
C) (-4)/2 - 1 = -2 - 1 = -3; (-4) - 1 = -5. (False, -3 ≠ -5)
D) 5(-4) + 10 = -10; 2(-4) - 2 = -10. (True)
Therefore, x/2 - 1 = x - 1 is not satisfied by x = -4.
7The present age of Ram is twice the present age of his son. If Ram's age 5 years ago was three times his son's age at that time, what is Ram's present age?
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Answer: 20 years
Hint: Let the son's present age be 'x'. Express Ram's present age in terms of 'x'. Then form an equation based on their ages 5 years ago.
Solution:
Let the son's present age be x years. Then Ram's present age is 2x years.
5 years ago, son's age was (x - 5) years. Ram's age was (2x - 5) years.
According to the problem, 5 years ago, Ram's age was three times his son's age: 2x - 5 = 3(x - 5).
Solve the equation: 2x - 5 = 3x - 15 => 15 - 5 = 3x - 2x => 10 = x.
Son's present age is 10 years. Ram's present age is 2x = 2 × 10 = 20 years.
8Consider the equation x + 5 = 12. If we subtract 5 from the left side, what must we do to the right side to maintain the equality?
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Answer: Subtract 5
Hint: To keep an equation balanced, any operation performed on one side must also be performed on the other side.
Solution:
The fundamental principle of solving equations is to maintain equality.
If an operation (addition, subtraction, multiplication, division) is performed on one side of the equation, the *same* operation must be performed on the other side.
Since 5 is subtracted from the left side, to maintain equality, 5 must also be subtracted from the right side.
This leads to x + 5 - 5 = 12 - 5, which simplifies to x = 7.
9Solve for y: (1/3)(6y - 9) = y + 4
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Answer: y = 7
Hint: First, distribute the fraction into the bracket. Then, proceed to solve the linear equation with variables on both sides.
Solution:
Distribute (1/3) on the left side: (1/3) × 6y - (1/3) × 9 = y + 4.
Simplify: 2y - 3 = y + 4.
Transpose terms: 2y - y = 4 + 3.
Simplify: y = 7.
10The perimeter of a rectangular park is 100 m. If its length is 10 m more than its width, what is the width of the park?
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Answer: 20 m
Hint: Recall the formula for the perimeter of a rectangle. Express length in terms of width using a variable.
Solution:
Let the width of the park be 'w' meters.
The length 'l' is 10 m more than its width, so l = w + 10 m.
The perimeter of a rectangle is P = 2(l + w).
Given P = 100 m, so 100 = 2((w + 10) + w).
Simplify: 100 = 2(2w + 10).
Divide by 2: 50 = 2w + 10.
Transpose: 50 - 10 = 2w => 40 = 2w.
Solve for w: w = 40 / 2 = 20 m.
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Tips for Linear Equations MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Linear Equations MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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