Welcome To My School Study
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.
Do You Know
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 teaches students how to solve equations involving one variable. These concepts form the foundation of algebra and help students develop logical reasoning and analytical skills.
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 widely used in mathematics and real-life situations such as age problems, money calculations, measurements, and logical reasoning. A strong understanding of equations helps students solve complex algebraic problems in higher classes.
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:
$$x+12=28$$
A) $$14$$
B) $$15$$
C) $$16$$
D) $$17$$
Answer:
$$16$$
Useful Formula for this Question:
If
$$x+a=b$$
then
$$x=b-a$$
Concept Behind This Question:
Students should isolate the variable by moving constants to the opposite side.
Step-by-Step Solution:
Given:
$$x+12=28$$
Subtract $$12$$ from both sides:
$$x=28-12$$
$$x=16$$
Therefore, the correct answer is:
$$16$$
Exam Tip:
Use the inverse operation to isolate the variable.
Q2. Solve:
$$x-9=22$$
A) $$29$$
B) $$31$$
C) $$33$$
D) $$35$$
Answer:
$$31$$
Useful Formula for this Question:
If
$$x-a=b$$
then
$$x=b+a$$
Concept Behind This Question:
Students should apply the transposition method correctly.
Step-by-Step Solution:
Given:
$$x-9=22$$
Add $$9$$ to both sides:
$$x=22+9$$
$$x=31$$
Therefore, the correct answer is:
$$31$$
Exam Tip:
A negative term becomes positive after transposition.
Q3. Solve:
$$4x=36$$
A) $$7$$
B) $$8$$
C) $$9$$
D) $$10$$
Answer:
$$9$$
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 of the variable.
Step-by-Step Solution:
Given:
$$4x=36$$
Divide both sides by $$4$$
$$x=\frac{36}{4}$$
$$x=9$$
Therefore, the correct answer is:
$$9$$
Exam Tip:
The coefficient multiplying the variable moves to the denominator.
Q4. Solve:
$$\frac{x}{7}=6$$
A) $$40$$
B) $$41$$
C) $$42$$
D) $$43$$
Answer:
$$42$$
Useful Formula for this Question:
If
$$\frac{x}{a}=b$$
then
$$x=ab$$
Concept Behind This Question:
Students should remove fractions by multiplying both sides.
Step-by-Step Solution:
Given:
$$\frac{x}{7}=6$$
Multiply both sides by $$7$$
$$x=6\times7$$
$$x=42$$
Therefore, the correct answer is:
$$42$$
Exam Tip:
Clear the denominator first before solving.
Q5. Solve:
$$3x+5=20$$
A) $$3$$
B) $$4$$
C) $$5$$
D) $$6$$
Answer:
$$5$$
Useful Formula for this Question:
Solve step-by-step by isolating the variable.
Concept Behind This Question:
Students should perform operations in the correct order.
Step-by-Step Solution:
Given:
$$3x+5=20$$
Subtract $$5$$ from both sides:
$$3x=15$$
Divide both sides by $$3$$
$$x=5$$
Therefore, the correct answer is:
$$5$$
Exam Tip:
Remove constants first, 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 whose highest power of the variable is 1.
2. What is a variable?
A variable is a symbol that represents an unknown value.
3. What is transposition?
Transposition is the process of moving a term from one side of an equation to the other by changing its sign.
4. How many solutions does a linear equation in one variable have?
Generally, it has one unique solution.
5. Why should we verify our answer?
Verification confirms that the obtained value satisfies the original equation.
Common Mistakes
❌ Changing signs incorrectly during transposition.
❌ Forgetting to divide by the coefficient.
❌ Arithmetic calculation mistakes.
❌ Not verifying the final answer.
❌ Solving both sides incorrectly.
Quick Revision Notes
✔ Linear equations contain variables with power 1.
✔ Use inverse operations to isolate the variable.
✔ Change signs during transposition.
✔ Divide by the coefficient after simplifying.
✔ Always verify the obtained solution.
✔ Linear equations are the foundation of algebra.
Conclusion
Linear Equations in One Variable is one of the most important chapters in Class 8 Mathematics. Understanding variables, equations, and transposition methods helps students solve algebraic problems efficiently and prepares them for advanced mathematical concepts. Regular MCQ practice improves accuracy, confidence, and problem-solving skills.
Related links
- 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
Latest Posts
- Class 7 Maths Chapter 3 Data Handling
- Class 9 Maths Chapter 3 Coordinate Geometry
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two
- Class 8 Maths Chapter 3 Understanding Quadrilaterals
- Class 7 Maths Chapter 3 Data Handling, data collection
Join Our Other Communities
Instagram , Youtube , Facebook
