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Practice Class 8 Maths Chapter 2 Linear Equations in One Variable MCQ Questions with Answers based on NCERT syllabus. Learn solving linear equations, transposition method, variables, constants, and algebraic expressions with detailed solutions for CBSE exams.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Linear Equations in One Variable
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Linear Equations in One Variable is an important chapter in Class 8 Mathematics that helps students solve unknown values using algebraic methods. Understanding equations improves logical reasoning and prepares students for advanced algebra topics.
What You Will Learn?
✔ Variables and Constants
✔ Linear Equations
✔ Transposition Method
✔ Solving Equations
✔ Verification of Solutions
✔ Algebraic Thinking
✔ Real-Life Applications of Equations
✔ Board Exam Preparation
Why This Topic Is Important?
Linear equations are used in daily-life calculations, age problems, distance calculations, and financial situations. Mastering this chapter strengthens mathematical thinking and problem-solving skills.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Solve:
$$x+18=45$$
A) $$25$$
B) $$26$$
C) $$27$$
D) $$28$$
Answer:
$$27$$
Useful Formula for this Question:
If
$$x+a=b$$
then
$$x=b-a$$
Concept Behind This Question:
Students should isolate the variable using subtraction.
Step-by-Step Solution:
Given:
$$x+18=45$$
Subtract $$18$$ from both sides:
$$x=45-18$$
$$x=27$$
Therefore, the correct answer is:
$$27$$
Exam Tip:
Use inverse operations to isolate the variable.
Q2. Solve:
$$x-14=19$$
A) $$31$$
B) $$32$$
C) $$33$$
D) $$34$$
Answer:
$$33$$
Useful Formula for this Question:
If
$$x-a=b$$
then
$$x=b+a$$
Concept Behind This Question:
Students should apply transposition correctly.
Step-by-Step Solution:
Given:
$$x-14=19$$
Add $$14$$ to both sides:
$$x=19+14$$
$$x=33$$
Therefore, the correct answer is:
$$33$$
Exam Tip:
A negative term becomes positive after transposition.
Q3. Solve:
$$5x=60$$
A) $$10$$
B) $$11$$
C) $$12$$
D) $$13$$
Answer:
$$12$$
Useful Formula for this Question:
If
$$ax=b$$
then
$$x=\frac{b}{a}$$
Concept Behind This Question:
Students should divide both sides by the coefficient.
Step-by-Step Solution:
Given:
$$5x=60$$
Divide both sides by $$5$$
$$x=\frac{60}{5}$$
$$x=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
Always divide by the coefficient attached to the variable.
Q4. Solve:
$$\frac{x}{8}=7$$
A) $$54$$
B) $$55$$
C) $$56$$
D) $$57$$
Answer:
$$56$$
Useful Formula for this Question:
If
$$\frac{x}{a}=b$$
then
$$x=ab$$
Concept Behind This Question:
Students should eliminate fractions using multiplication.
Step-by-Step Solution:
Given:
$$\frac{x}{8}=7$$
Multiply both sides by $$8$$
$$x=7\times8$$
$$x=56$$
Therefore, the correct answer is:
$$56$$
Exam Tip:
Multiply both sides by the denominator to remove fractions.
Q5. Solve:
$$4x+8=40$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
$$8$$
Useful Formula for this Question:
Solve step-by-step by isolating the variable.
Concept Behind This Question:
Students should remove constants before dividing.
Step-by-Step Solution:
Given:
$$4x+8=40$$
Subtract $$8$$ from both sides:
$$4x=32$$
Divide both sides by $$4$$
$$x=8$$
Therefore, the correct answer is:
$$8$$
Exam Tip:
First remove the constant term, then divide by the coefficient.
Important Formulas & Concepts
1. Linear Equation in One Variable
$$ax+b=0,\quad a\ne0$$
2. Addition Property
If
$$a=b$$
then
$$a+c=b+c$$
3. Subtraction Property
If
$$a=b$$
then
$$a-c=b-c$$
4. Multiplication Property
If
$$a=b$$
then
$$ac=bc$$
5. Division Property
If
$$a=b,\quad c\ne0$$
then
$$\frac{a}{c}=\frac{b}{c}$$
6. Verification Rule
Substitute the value of the variable into the original equation to verify the solution.
FAQs
1. What is a linear equation?
A linear equation is an equation in which the highest power of the variable is 1.
2. What is transposition?
Transposition means moving a term from one side of the equation to the other by changing its sign.
3. What is a variable?
A variable is a symbol representing an unknown value.
4. Why do we verify solutions?
Verification ensures that the obtained answer satisfies the original equation.
5. Can a linear equation have more than one variable?
Yes, but this chapter focuses only on one variable.
Common Mistakes
❌ Changing signs incorrectly.
❌ Forgetting to divide by the coefficient.
❌ Arithmetic errors.
❌ Not checking the final answer.
❌ Solving operations in the wrong order.
Quick Revision Notes
✔ Linear equations contain variables with power 1.
✔ Use inverse operations to solve equations.
✔ Change signs while transposing terms.
✔ Remove constants before dividing.
✔ Verify the final answer whenever possible.
✔ Practice regularly to improve speed and accuracy.
Conclusion
Linear Equations in One Variable is a fundamental algebra chapter that helps students solve unknown quantities logically. A strong understanding of equations improves problem-solving skills and creates a solid foundation for higher mathematics. Regular MCQ practice enhances confidence and exam performance.
Related links
- Class8 Maths Chapter2 Linear Equations in One Variable MCQ – Part 1
- Class 8 Maths Chapter 1 Rational Numbers- Part 10
- Class 8 Maths Chapter 1 Rational Numbers – Part 9
- Class 8 Maths Chapter 1 Rational Numbers – Part 8
- Class 8 Maths additive inverse, multiplicative inverse MCQ – Part 7
- Class 8 Maths Chapter 1 properties of rational numbers, additive inverse – Part 6
- Class 8 Maths Chapter 1 Rational Numbers multiplicative – Part 5
- Class 8 Maths Chapter 1 Rational Numbers – Part 4
- Class 8 Maths Chapter 1 Rational Numbers, Additive inverse -Part 3
- Class 8 Maths Chapter 1 Rational Numbers – Part 2
- Class 8 Maths Chapter 1 Rational Numbers- part 1
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