Class 8th · Mathematics · Chapter 2

Linear equations in one variable – Notes, MCQs, Quiz & Worksheet

Start MCQ Practice Download Worksheet
Overview

What is Linear equations in one variable?

Linear Equations in One Variable are algebraic equations that contain only one variable, and the highest power (exponent) of the variable is 1. The objective is to find the value of the variable that makes the equation true.

A linear equation in one variable is generally written in the form ax + b = 0, where a and b are constants, x is the variable, and a is not equal to zero.

Examples include:

x + 5 = 12
3x - 7 = 11
2(x + 4) = 18

To solve a linear equation, perform the same mathematical operation on both sides of the equation to isolate the variable. Common operations include addition, subtraction, multiplication, and division.

Linear equations in one variable are widely used in everyday life to solve problems involving age, money, distance, time, shopping, and budgeting. Learning this topic helps develop logical thinking and provides a strong foundation for more advanced algebra and mathematics.

Exam relevance

Linear equations in one variable carries steady weightage in Class 8th exams. Practising its MCQs and important questions is one of the fastest ways to secure marks from this chapter.

Need formulas?

Get all the important Mathematics formulas in one quick-revision sheet.

Open Formula Sheets
MCQ Practice

Practice MCQs – Linear equations in one variable

Attempt these multiple-choice questions, then reveal the answer to check yourself.

Q1.Solve for z: z/5 - 2 = 0.
A.10
B.5
C.2
D.-10
Answer: 10
Q2.Rohan is 5 years older than his sister Priya. If the sum of their ages is 27, how old is Priya?
A.11
B.16
C.22
D.10
Answer: 11
Q3.If a = b, then a + c = b + c. This is an example of which property?
A.Commutative Property
B.Associative Property
C.Addition Property of Equality
D.Distributive Property
Answer: Addition Property of Equality
Q4.The ratio of two numbers is 2:3. If their sum is 30, what is the larger number?
A.12
B.18
C.10
D.15
Answer: 18
Q5.An equation is balanced when:
A.The left side is equal to the right side.
B.The variable is isolated.
C.All numbers are positive.
D.There are no fractions.
Answer: The left side is equal to the right side.
Q6.Sara is currently x years old. In 5 years, she will be 18. Which equation represents this?
A.x - 5 = 18
B.x + 5 = 18
C.5x = 18
D.x/5 = 18
Answer: x + 5 = 18
Q7.The sum of three numbers is 30. The second number is twice the first, and the third number is 6 more than the first. What is the first number?
A.4
B.6
C.8
D.12
Answer: 6
Q8.John has Rs. 10 more than Mike. Together they have Rs. 60. How much money does Mike have?
A.Rs. 20
B.Rs. 25
C.Rs. 30
D.Rs. 35
Answer: Rs. 25
Q9.Identify the property: a(b + c) = ab + ac
A.Commutative Property
B.Associative Property
C.Distributive Property
D.Identity Property
Answer: Distributive Property
Q10.A father is three times as old as his son. If the sum of their ages is 48, how old is the son?
A.12
B.16
C.24
D.36
Answer: 12
Q11.Which equation has x = 2 as its solution?
A.3x + 1 = 6
B.2x - 3 = 1
C.x + 4 = 7
D.5x - 2 = 12
Answer: 2x - 3 = 1
Q12.What is the main goal when solving a linear equation?
A.To find multiple solutions.
B.To make both sides of the equation equal to zero.
C.To isolate the variable on one side.
D.To eliminate all numbers.
Answer: To isolate the variable on one side.
Q13.Solve: (x - 3)/4 = (x - 5)/2.
A.7
B.-7
C.9
D.-9
Answer: 7
Q14.What does 'isolate the variable' mean?
A.To move the variable to the right side of the equation.
B.To make the variable stand alone on one side of the equation.
C.To make the variable zero.
D.To multiply the variable by zero.
Answer: To make the variable stand alone on one side of the equation.
Q15.The difference between two numbers is 8. If the larger number is three times the smaller number, what is the smaller number?
A.4
B.8
C.12
D.16
Answer: 4
Q16.If 3 pens cost Rs. 45, what is the cost of one pen?
A.Rs. 10
B.Rs. 15
C.Rs. 20
D.Rs. 42
Answer: Rs. 15
Q17.What is the degree of a linear equation in one variable?
A.0
B.1
C.2
D.3
Answer: 1
Q18.Which of the following is a linear equation in one variable?
A.x² + 2x = 5
B.3x - 7 = 0
C.x + y = 10
D.5/x + 2 = 3
Answer: 3x - 7 = 0
Q19.If x + 5 = 12, what is the value of x?
A.7
B.17
C.-7
D.5
Answer: 7
Q20.Solve for x: x - 3 = 8.
A.5
B.11
C.-5
D.-11
Answer: 11
Q21.Find the value of y if 4y = 20.
A.5
B.16
C.24
D.80
Answer: 5
Q22.What is the solution to x/2 = 9?
A.4.5
B.11
C.18
D.7
Answer: 18
Q23.Solve the equation 2x + 1 = 7.
A.3
B.4
C.2
D.6
Answer: 3
Q24.When 6 is transposed from the left side to the right side of the equation x + 6 = 10, what happens to its sign?
A.It remains positive.
B.It changes to negative.
C.It becomes zero.
D.It becomes multiplication.
Answer: It changes to negative.
Q25.Which value of x makes the equation 5x - 2 = 13 true?
A.2
B.3
C.4
D.5
Answer: 3
Q26.A number increased by 7 is 15. What is the number?
A.22
B.8
C.7
D.15
Answer: 8
Q27.Three times a number is 27. What is the number?
A.81
B.24
C.9
D.30
Answer: 9
Q28.Solve for p: p - (-4) = 10.
A.6
B.14
C.-6
D.-14
Answer: 6
Q29.Solve for m: -3m = 18.
A.6
B.-6
C.15
D.-15
Answer: -6
Q30.Simplify and solve: 2x + 3x = 25.
A.20
B.5
C.10
D.25
Answer: 5
Practice More MCQs
Quiz

Take a Linear equations in one variable Quiz

A short, timed quiz with instant scoring — perfect for checking how well you know the chapter.

Linear equations in one variable Quiz

Attempt a 10–20 question quiz on Linear equations in one variable. Try to finish within 15 minutes, get instant scoring, and see which topics need more revision.

Start Quiz Now

Quiz Test

Take a timed quiz with instant scoring to test your speed and accuracy.

Start Quiz
Important Questions

Most Expected Linear equations in one variable Questions

High-weightage and frequently asked questions to prioritise before exams.

Quick Revision

Linear equations in one variable – Quick Revision Notes

A one-page recap to revise the whole chapter in minutes.

  • Linear equations in one variable is part of the Class 8th Mathematics syllabus and carries steady exam weightage.
  • Re-read all formulas, laws and definitions from this chapter.
  • Re-attempt the MCQs you got wrong and solve one worksheet.
  • Finish with a short quiz to confirm you remember everything.
Explore More

Explore More Mathematics Resources

Class 8th Home Class 8th Mathematics Formula Sheets Study Tools
Educational intent

Created to help Class 8th students learn and revise Linear equations in one variable from Mathematics using notes, practice questions and free study tools.

Accuracy & learning-first

Our content is prepared and reviewed by experienced educators and kept aligned with the latest NCERT / CBSE syllabus and exam pattern.

Student-focused note

These resources support your school learning and self-study. Always cross-check with your prescribed textbook and your teacher's guidance for board exams.