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Important Questions

Linear Equations in One Variable

Gujarat Board · Class 8 · Mathematics

Most important questions from Linear Equations in One Variable for Gujarat Board Class 8 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

45 questions5 concepts

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45 Questions·
multiple choice

Sample Questions

1multiple choice
1 marks

Solve: 8x + 4 = 3(x - 1) + 7. What is the value of x?

Show answer

x = 0

Step 1: We have 8x + 4 = 3(x - 1) + 7. First expand the bracket on RHS. Step 2: RHS = 3x - 3 + 7 = 3x + 4. Step 3: Equation becomes 8x + 4 = 3x + 4. Step 4: Transpose: 8x - 3x = 4 - 4 → 5x = 0 → x = 0. Step 5: Verify — LHS = 8(0) + 4 = 4; RHS = 3(0-1) + 7 = -3 + 7 = 4. LHS = RHS ✓ Common mistake: Not expanding the bracket correctly — students may forget to multiply 3 × (-1) = -3.

2multiple choice
1 marks

Solve: x = (4/5)(x + 10). What is the value of x?

Show answer

x = 40

Step 1: We have x = (4/5)(x + 10). Multiply both sides by 5 to remove the fraction. Step 2: 5x = 4(x + 10). Step 3: Expand: 5x = 4x + 40. Step 4: Transpose: 5x - 4x = 40 → x = 40. Step 5: Verify — RHS = (4/5)(40 + 10) = (4/5)(50) = 40 = LHS ✓ Common mistake: Students multiply only the numerator by 5 and forget to multiply (x+10), leading to incorrect expansion.

3multiple choice
1 marks

Solve: (2x/3) + 1 = (7x/15) + 3. What is the value of x?

Show answer

x = 10

Step 1: We have (2x/3) + 1 = (7x/15) + 3. LCM of 3 and 15 is 15. Step 2: Multiply every term by 15: 15×(2x/3) + 15×1 = 15×(7x/15) + 15×3. Step 3: Simplify: 10x + 15 = 7x + 45. Step 4: Transpose: 10x - 7x = 45 - 15 → 3x = 30 → x = 10. Step 5: Verify — LHS = (20/3) + 1 = 23/3; RHS = (70/15) + 3 = 14/3 + 9/3 = 23/3. LHS = RHS ✓ Common mistake: Using LCM incorrectly or multiplying only some terms by 15.

4multiple choice
1 marks

Solve: (6x + 1)/3 + 1 = (x - 3)/6. What is the value of x?

Show answer

x = -1

Step 1: LCM of 3 and 6 is 6. Multiply every term by 6. Step 2: 6×(6x+1)/3 + 6×1 = 6×(x-3)/6 → 2(6x+1) + 6 = (x-3). Step 3: Expand: 12x + 2 + 6 = x - 3 → 12x + 8 = x - 3. Step 4: Transpose: 12x - x = -3 - 8 → 11x = -11 → x = -1. Step 5: Verify — LHS = (6(-1)+1)/3 + 1 = (-5/3) + 1 = -2/3; RHS = (-1-3)/6 = -4/6 = -2/3. LHS = RHS ✓ Common mistake: Not expanding 2(6x+1) properly — missing 2×1 = 2.

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Frequently Asked Questions

What are the important topics in Linear Equations in One Variable for Gujarat Board Class 8 Mathematics?
Key topics in Linear Equations in One Variable include Chapter Overview: Linear Equations in One Variable, Linear Equations in One Variable - Concept Overview, Linear Equations in One Variable — Complete Concept Map. These are the concepts Gujarat Board Class 8 examiners draw on most — study them first, then practise related questions.
How to score full marks in Linear Equations in One Variable — Gujarat Board Class 8 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Linear Equations in One Variable?
There are 45 practice questions available for Linear Equations in One Variable. These cover multiple question types including MCQs, short answer, and long answer questions.

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