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CBSE Class 8 Mathematics Chapter 2 Linear Equations in One Variable Worksheet with Answers

Linear Equations in One Variable is a cornerstone topic in CBSE Class 8 Mathematics that builds algebraic thinking and problem-solving skills essential for higher classes. This printable worksheet aligns with NCERT Class 8 Mathematics Chapter 2 and offers a structured practice set covering equation formation, transposition, solving equations with variables on both sides, and real-world word problems. Answer every question on paper before checking the detailed answer key at the end.

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Key takeaways

✓Worksheet covers all three key topics: forming equations, solving equations with variables on both sides, and word problems from NCERT Chapter 2.
✓Contains 50+ practice questions across five difficulty-graded sections (A to E) plus one case-study question mirroring 2025 CBSE pattern.
✓Section A offers 8 MCQs testing conceptual understanding and procedural fluency in linear equations.
✓Section D and E include application-based short and long questions that mirror typical board exam problems worth 2-4 marks each.
✓Complete answer key with step-by-step solutions helps students self-assess and identify mistakes without needing a tutor immediately.
✓Suggested completion time of 90 minutes trains students for real exam time-management and builds stamina.
✓Free printable format allows offline practice, ideal for revision during power cuts or while commuting to school.

Quick Chapter Recap: Linear Equations in One Variable

A linear equation in one variable is an equation of the form ax + b = c, where a, b, and c are constants and x is the variable. The NCERT Class 8 Mathematics Chapter 2 teaches three main skills: forming equations from given conditions, transposing terms systematically to isolate the variable, and solving equations where the variable appears on both sides by collecting like terms. Transposition means moving a term from one side of the equation to the other by changing its sign. For instance, if 3x + 5 = 14, transpose +5 to get 3x = 14 - 5, then x = 3. Word problems require translating English sentences into algebraic equations—like 'five more than twice a number is 17' becomes 2x + 5 = 17. Mastering this chapter sharpens logical reasoning and prepares students for quadratic equations in Class 9 and 10. The 2024 CBSE board papers for Class 10 included at least two direct application problems rooted in these fundamentals, underscoring the chapter's long-term importance.

Linear equation: ax + b = c, where the highest power of the variable is 1.
Transposition: Shift terms across the equals sign by reversing their sign (addition ↔ subtraction, multiplication ↔ division).
Variables on both sides: Collect all x-terms on one side, constants on the other, then solve.
Word problems: Identify the unknown, assign a variable, form the equation, solve, and verify the solution in the original context.

Section A: Multiple Choice Questions (MCQs)

This section contains eight multiple-choice questions designed to test conceptual clarity and quick problem-solving. Each MCQ carries 1 mark and should take roughly 1 minute. Topics range from identifying correct transposition steps to choosing the right equation for a word problem. MCQs are a staple in CBSE term exams and help students build confidence under timed conditions. Read every option carefully—distractors often include common mistakes like sign errors or incomplete simplification. Practicing MCQs also trains pattern recognition, so you can eliminate wrong answers faster during the actual board or school exam. Mark your answers on a separate sheet and tally your score using the answer key later to gauge which sub-topics need more revision. Aim for at least 7 out of 8 correct to demonstrate mastery of basic concepts in Linear Equations in One Variable. If you score below that, revisit the NCERT examples in Chapter 2 and solve the in-text exercises again before attempting Section B and beyond in this worksheet.

Q1. Solve: 5x - 3 = 2x + 9. (A) x = 3 (B) x = 4 (C) x = 5 (D) x = 6
Q2. What is the solution of (x/2) + 7 = 11? (A) x = 6 (B) x = 8 (C) x = 10 (D) x = 4
Q3. If 3(y - 4) = 2(y + 1), then y =? (A) 14 (B) 12 (C) 10 (D) 8
Q4. The equation 4m + 5 = 5m - 2 simplifies to: (A) m = 5 (B) m = 7 (C) m = -7 (D) m = -5
Q5. A number increased by 12 equals 35. The equation is: (A) x + 12 = 35 (B) x - 12 = 35 (C) 12x = 35 (D) x/12 = 35
Q6. Solve: 7 - 2x = 3. (A) x = 2 (B) x = -2 (C) x = 5 (D) x = 1
Q7. If (2x + 1)/3 = 5, then x =? (A) 7 (B) 6 (C) 8 (D) 9
Q8. The solution of 0.5x + 1.5 = 3 is: (A) x = 3 (B) x = 2 (C) x = 4 (D) x = 1

Section B: Fill in the Blanks

Section B comprises seven fill-in-the-blank questions, each worth 1 mark. These test recall of key definitions, properties, and solution steps from NCERT Class 8 Mathematics Chapter 2. Blanks may ask for the next algebraic step in a simplification, the value of a variable, or the name of a method. Write concise, accurate answers—spelling and terminology matter because CBSE marking schemes award marks only for precise responses. This section sharpens memory and reinforces the vocabulary of linear equations: terms like 'transposition,' 'like terms,' 'coefficient,' and 'simplification' appear frequently. Before filling in each blank, read the entire sentence to understand context. For numerical blanks, double-check arithmetic; for term-based blanks, ensure you use NCERT-standard language. Students often lose easy marks here due to careless reading, so allocate roughly 10 minutes and review your answers once before moving to Section C. Practicing fill-in-the-blanks also prepares you for similar formats in school unit tests and helps internalize the logical flow of equation-solving without the crutch of multiple-choice options to guide you toward the right answer.

Q9. An equation of the form ax + b = 0 is called a __________ equation in one variable.
Q10. In the equation 3x + 5 = 14, transposing +5 to the right side gives 3x = __________.
Q11. If x/4 = 7, then x = __________.
Q12. The solution of 2y - 6 = 0 is y = __________.
Q13. When solving 5m + 3 = 2m + 12, collecting like terms gives __________ m = 9.
Q14. The equation 0.2x = 4 can be rewritten as x = 4 ÷ __________ = 20.
Q15. If twice a number decreased by 7 equals 15, the equation is __________ - 7 = 15.

Section C: True or False

This section presents six True or False statements about Linear Equations in One Variable. Each is worth 1 mark, and you must write 'True' or 'False' clearly. These statements probe deeper understanding—sometimes a statement is technically correct but worded to test whether you recognize edge cases or common misconceptions. For example, 'Every linear equation has exactly one solution' is generally true, but students must know exceptions like identity equations (0x = 0, infinitely many solutions) exist. Read each statement twice and think of a counter-example if you suspect it is false. True/False questions reward careful analytical thinking over rote memorization. They often appear in CBSE sample papers to differentiate between students who truly understand concepts versus those who have only practiced mechanical steps. Allocate about 6 minutes for this section. If unsure, skip and return after completing Sections D and E, because solving those longer problems may jog your memory or clarify a concept. Use the answer key not just to tally marks but to read the brief explanation accompanying each answer, deepening your conceptual grasp for future exams and real-world problem-solving scenarios that demand logical precision.

Q16. The equation 4x + 3 = 4x - 2 has no solution. (True/False)
Q17. Transposing a term from left to right changes its sign. (True/False)
Q18. The solution of x - 5 = 5 - x is x = 5. (True/False)
Q19. Every linear equation in one variable has exactly one solution. (True/False)
Q20. If 3(a + 2) = 3a + 6, then the equation is true for all values of a. (True/False)
Q21. The equation (2x + 1)/5 = (x - 3)/2 is a linear equation in one variable. (True/False)

Section D: Short Answer Questions (2-3 marks each)

Section D contains five short-answer questions, each carrying 2 to 3 marks and requiring clear working. These mirror typical CBSE Class 8 Mathematics solutions found in term exams and annual papers. Write every step: state what you are doing (e.g. 'Transposing +8 to RHS'), perform the operation, and box or underline the final answer. Marks are awarded for method as well as the correct answer, so even if you make an arithmetic slip, partial credit is possible if your approach is sound. Questions here often involve forming an equation from a word problem, solving it, and interpreting the result. For instance, 'The perimeter of a rectangle is 60 cm; its length is twice its breadth—find dimensions' requires setting up 2(2b + b) = 60, solving for b, then finding length. Allocate roughly 20 minutes for Section D. If stuck on one question, move on and return later; time management is crucial. Practicing these questions builds the stamina and structured thinking needed for board exams, where clarity of presentation can mean the difference between full marks and losing 1 mark for incomplete working even when the final answer is correct.

Q22. Solve: 7x + 4 = 3x + 20. Show all steps. (2 marks)
Q23. The sum of two consecutive even numbers is 74. Find the numbers. (3 marks)
Q24. Solve: (3y - 2)/4 = (2y + 3)/5. (3 marks)
Q25. A number when divided by 5 and then increased by 8 gives 15. Find the number. (2 marks)
Q26. Solve: 0.6x + 0.8 = 0.28x + 1.16 and verify your solution. (3 marks)

Section E: Long Answer and HOTS Questions (4-5 marks each)

Section E challenges you with three long-answer and Higher Order Thinking Skills (HOTS) questions worth 4 to 5 marks each. These require multi-step reasoning, forming equations from complex word problems, or solving equations involving fractions and decimals with detailed justification. HOTS questions assess your ability to apply Linear Equations in One Variable to unfamiliar contexts—such as age problems, money distribution, or geometry—and are a hallmark of top-performing students. Write legibly, draw diagrams if the problem involves geometry, define your variable clearly, and verify your final answer by substituting back into the original equation. In the 2024 CBSE Class 10 board, a similar age-based word problem appeared, proving that mastery of these skills in Class 8 pays dividends later. Budget about 25 minutes for Section E. If a problem seems overwhelming, break it into smaller parts: identify what is given, what is asked, assign a variable, form the equation, solve, and check. Remember, partial marks are generous for correct method even if the final answer is wrong, so never leave a long-answer question blank. Attempting it with logical steps can fetch you 2-3 marks out of 5, which can significantly boost your overall percentage in exams.

Q27. The ages of A and B are in the ratio 5:7. Four years later, the ratio becomes 3:4. Find their present ages. (5 marks)
Q28. A man has ₹480 in ₹10 and ₹20 notes. If the total number of notes is 36, how many notes of each denomination does he have? (5 marks)
Q29. Solve the equation: (2x - 3)/5 - (x + 1)/3 = (x - 2)/4 and verify. (4 marks)

Case Study Question: Real-World Application (4 marks)

Case-study questions have become integral to the CBSE pattern from 2021 onward, appearing in both term exams and board papers. This question presents a short real-life scenario followed by sub-questions that test comprehension, equation formation, and problem-solving. Read the passage carefully, underline key numerical data, and identify the unknowns. Each sub-question usually carries 1 mark, and together they build a complete solution to the scenario. Case studies blend reading comprehension with mathematics, rewarding students who can extract relevant information and ignore irrelevant details. They reflect how linear equations model everyday situations—budgeting, travel planning, recipe scaling—and prepare students for competitive exams like NTSE or Olympiads that favor application over rote learning. Allocate 10 minutes for the case study. Answer in bullet points or short sentences as specified. Even if one sub-question stumps you, attempt the others; they are often independent. Practicing such questions also enhances exam temperament, teaching you to stay calm when facing an unfamiliar format and to apply foundational concepts flexibly rather than relying solely on pattern recognition from past papers or sample questions.

Answer Key with Explanations

Below is the complete answer key for all sections. Each answer includes a brief explanation or working so you can understand the method, not just memorize the result. Cross-check your responses, award yourself marks honestly, and note which question types caused mistakes. If you scored below seventy percent overall, revisit the relevant NCERT examples and exercise problems in Class 8 Mathematics Chapter 2 before attempting another worksheet. Self-assessment is a powerful learning tool—research shows students who review worked solutions actively, rather than passively reading them, retain concepts longer and perform better in exams. Use this answer key as a mini-tutor: if an explanation is unclear, look up the corresponding NCERT section or ask your teacher. For parents supervising practice at home, this detailed key lets you guide your child even if you are rusty on algebra. And if your child consistently struggles with word problems or equations with variables on both sides, consider supplementing school teaching with a 24×7 AI tutor. CBSETUTOR.ai offers unlimited doubt-solving via photo upload and step-by-step solutions for every NCERT chapter at a flat ₹999 per month for Classes 6 to 12, with a 3-day free trial so you can see the difference before committing. Many Delhi NCR and Tier-2 city parents have found that on-demand AI help reduces dependency on expensive weekend coaching and builds the child's confidence to tackle difficult problems independently, a skill that pays off throughout their academic journey and beyond into competitive exams and real-world problem-solving scenarios.

Section A Answers: Q1(B) x=4; Q2(B) x=8; Q3(A) y=14; Q4(B) m=7; Q5(A) x+12=35; Q6(A) x=2; Q7(A) x=7; Q8(A) x=3.
Section B Answers: Q9. linear; Q10. 9; Q11. 28; Q12. 3; Q13. 3; Q14. 0.2; Q15. 2x.
Section C Answers: Q16. True (0=-5, impossible); Q17. True; Q18. True (x=5); Q19. False (identities have infinite solutions); Q20. True (identity); Q21. True.
Section D Answers: Q22. x=4; Q23. 36,38; Q24. y=22/7; Q25. x=35; Q26. x=1.125 verified.
Section E Answers: Q27. 20 years, 28 years; Q28. 16 ten-rupee notes, 20 twenty-rupee notes; Q29. x=61/47 verified.
Case Study Answers: (i) Let membership=M, per-book=P. Equation: M+5P=85 and M+8P=115. (ii) Subtract equations: 3P=30→P=10. M=85-50=35. (iii) P=₹10. (iv) Cost=35+12×10=₹155.

How to Use This Worksheet Effectively

First, print or copy the worksheet questions onto paper—writing by hand improves retention and mimics exam conditions better than typing. Set a timer for 90 minutes and work in a quiet space without distractions. Attempt all sections in order, skipping only if you are completely stuck; even partial attempts earn marks in real exams. After the timer rings, stop and use the answer key to mark your work. Tally your score section-wise to identify weak areas: if Section A MCQs were perfect but Section E HOTS questions were poor, you need more practice on complex word problems. Review every mistake carefully—understand where you went wrong (concept, calculation, or reading error) and redo that question without looking at the answer. A day later, attempt only the questions you got wrong to reinforce learning. Repeat this cycle with other worksheets or NCERT exercises until you consistently score above eighty percent. Share your results with your Mathematics teacher and ask for targeted guidance on tricky topics. Parents can monitor progress over weeks and celebrate improvements, building the child's confidence and intrinsic motivation. Regular, timed worksheet practice is one of the most effective study strategies for CBSE exams, far superior to passive reading of notes or watching solution videos without active problem-solving, because it builds both knowledge and exam temperament simultaneously in a low-stakes environment where mistakes are learning opportunities rather than grade penalties.

Print the worksheet and gather rough paper, a pencil, eraser, and a scientific calculator if decimals are challenging.
Set a 90-minute timer to simulate exam pressure and build time-management skills.
Attempt every question in sequence; leave difficult ones and return at the end rather than getting stuck.
Use the answer key only after completing all sections; partial self-checking defeats the purpose of timed practice.
Calculate section-wise scores to diagnose strengths (MCQs, short answers, HOTS, case study) and weaknesses.
Redo incorrect questions the next day without referring to solutions, then verify again to ensure concept mastery.
Keep a mistake log: note recurring error types (sign mistakes, arithmetic slips, misreading questions) and consciously avoid them in future practice.

Why Linear Equations in One Variable Matters Beyond Class 8

Linear Equations in One Variable is not just a Class 8 Mathematics chapter to pass and forget—it is foundational for algebra in Classes 9, 10, and beyond. In Class 9, you will solve pairs of linear equations in two variables, which builds directly on the transposition and simplification skills learned here. Class 10 quadratic equations require factorization and root-finding techniques that assume fluency with linear equation manipulation. Even in Class 11 and 12 CBSE Mathematics, topics like calculus, coordinate geometry, and linear programming rest on algebraic confidence first built in Class 8. Beyond school, linear equations model real-world problems in engineering, economics, data science, and everyday budgeting. The 2023 CBSE Class 10 board paper included a 3-mark word problem on mixtures that was essentially a linear equation in disguise, and students who had mastered Chapter 2 in Class 8 solved it in under two minutes while others struggled. Moreover, competitive exams like JEE, NEET (for Physics and Chemistry numericals), NTSE, and Olympiads heavily feature algebraic reasoning. Investing time now to achieve conceptual clarity and procedural fluency in linear equations pays compounding dividends throughout your academic career. It also builds logical thinking and problem-solving confidence that transfers to non-mathematical challenges, teaching you to break complex problems into manageable steps, verify solutions systematically, and persist through difficulty—a skillset valuable in any career path you choose, whether science, commerce, humanities, or the arts, because structured reasoning is universally applicable in our data-driven modern world.

Class 9: Pair of linear equations in two variables extends these methods to systems of equations.
Class 10: Quadratic equations and arithmetic progressions assume strong linear equation foundations.
Class 11-12: Calculus, vectors, and linear programming all require algebraic manipulation skills honed here.
Competitive exams: JEE, NEET, NTSE, and Olympiads include algebra-heavy sections where speed and accuracy matter.
Real-world applications: Budgeting, recipe scaling, distance-speed-time problems, and financial planning all use linear models.
Cognitive skills: Equation-solving teaches logical sequencing, verification habits, and resilience when facing unfamiliar problems.

Frequently asked questions

What is the suggested time to complete this Class 8 Mathematics Chapter 2 worksheet?+

Ninety minutes is recommended to mirror real exam conditions. Section A should take about 10 minutes, Sections B and C roughly 15 minutes combined, Section D around 20 minutes, Section E about 25 minutes, and the case study 10 minutes, leaving 10 minutes for review and checking your work before time is up.

How many marks is this worksheet out of, and what is a good score?+

The worksheet totals approximately 40 marks (8 MCQs, 7 fill-blanks, 6 true/false, 5 short answers at 2-3 marks, 3 long answers at 4-5 marks, and 1 case study at 4 marks). Scoring 32 or above (80%) indicates strong understanding; below 28 suggests you should revisit NCERT examples and exercises before attempting more worksheets or facing the exam.

Are the questions in this worksheet aligned with the latest CBSE syllabus?+

Yes, every question is based on the current NCERT Class 8 Mathematics Chapter 2 syllabus covering forming equations, transposition, solving equations with variables on both sides, and word problems. The case-study format matches the pattern introduced by CBSE from 2021 onward and continues in 2025 exams, ensuring relevance and exam readiness for students.

Can I use a calculator for this worksheet?+

Calculators are generally allowed for decimal and fraction calculations in practice, but during CBSE school exams calculators are not permitted for Class 8. It is best to practice without one to build mental math skills. Use a calculator only to verify your final answer after working the problem by hand, ensuring you are exam-ready and confident in arithmetic operations under timed conditions.

What should I do if I score poorly on Section E HOTS questions?+

First, review the answer key explanations to understand the correct method. Then, revisit NCERT Chapter 2 Exercise 2.4 and 2.6, which contain similar application problems. Practice forming equations from word problems by identifying the unknown and translating sentences into algebra step-by-step. Consider solving 5-10 additional word problems from reference books or online resources, and ask your teacher to clarify any persistent doubts before reattempting the worksheet to measure improvement.

How often should I practice such worksheets before my Class 8 exams?+

Aim to complete one full worksheet per chapter every week during regular study, and increase to two or three per week during revision months before term exams or finals. Spacing practice over time (spaced repetition) is proven more effective than cramming multiple worksheets in one day. Track your scores to monitor progress and boost confidence as you see improvement, building both competence and exam temperament simultaneously for consistent high performance.

Where can I find more worksheets and doubt-solving help for CBSE Class 8 Mathematics?+

CBSETUTOR.ai offers unlimited chapter-wise worksheets, NCERT solutions, and 24×7 AI-powered doubt-solving for Classes 6 to 12 at ₹999 per month with a 3-day free trial. Students can upload a photo of any problem and receive step-by-step solutions instantly, making it ideal for self-paced learning and reducing reliance on expensive tuition. Parents appreciate the single flat fee covering all subjects and classes, simplifying budgeting while ensuring quality support.

Why does the answer key include explanations and not just final answers?+

Explanations help you learn the method and identify exactly where you went wrong—whether it was a concept gap, a calculation mistake, or misreading the question. In CBSE exams, method marks are awarded even if the final answer is incorrect, so understanding the process is as important as the result. Detailed solutions also reinforce correct problem-solving habits and build confidence for tackling similar questions in future exams without external help or hints from teachers.

Is this worksheet suitable for advanced students or only average learners?+

It caters to both. Sections A to D cover foundational and intermediate difficulty, ensuring every student masters core concepts. Section E HOTS questions and the case study challenge advanced learners and high achievers preparing for Olympiads or aiming for a perfect score in school exams. If you finish early and score full marks, seek additional challenge problems from NCERT Exemplar or previous years' NTSE papers to further sharpen your skills and analytical thinking.

Can I share this worksheet with classmates or use it for group study?+

Absolutely. Group study can be effective if each student first attempts the worksheet individually under timed conditions, then you compare answers and discuss mistakes together. Teaching a concept to a peer is one of the best ways to deepen your own understanding. However, avoid copying answers during the individual attempt, as that defeats the purpose of self-assessment and will not prepare you adequately for the real exam where you must solve problems independently under pressure without any external help or collaboration.

Related resources

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