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Class 8 Mathematics Chapter 02 Linear Equations in One Variable

This quiz on Linear Equations in One Variable for Class 8 Mathematics is designed to assess students' understanding of solving equations involving a single variable. It covers key concepts such as the formation of linear equations, solving equations using different operations, applications in real-life problems, and equations with variables on both sides. Through multiple-choice and short-answer questions, students will test their problem-solving skills while receiving instant feedback and explanations for incorrect answers. The quiz also includes supplementary notes and video links for better clarity. If you score 50% or above, you will receive a Certificate of Achievement by mail. All the best! Take the quiz and identify your weaker topics and subtopics.

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Category: Introduction

1. Solve for $x$ in the equation $3x - 7 = 14$.

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Category: Introduction

2. (A) The equation $3x + 5 = 11$ is a linear equation in one variable.
(R) A linear equation in one variable has the highest power of the variable as 1.

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Category: Introduction

3. Which of the following is a linear expression in one variable?

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Category: Introduction

4. Which of the following is a linear equation in one variable?

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Category: Introduction

5. Solve for $x$: $\frac{3x - 4}{2} + \frac{5x + 7}{3} = 10$.

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Category: Definition of algebraic expressions and equations

6. In the equation $\frac{y}{2} + \frac{z}{2} = 6$, what is the Left Hand Side (LHS)?

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Category: Definition of algebraic expressions and equations

7. Which of the following is a linear expression in one variable?

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Category: Definition of algebraic expressions and equations

8. Which of the following is an algebraic expression?

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Category: Definition of algebraic expressions and equations

9. Which of the following is a linear equation in one variable?

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Category: Definition of algebraic expressions and equations

10. The equation $\frac{z - 4}{2} = 3$ has a solution where $z$ equals?

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Category: Difference between expressions and equations

11. Which of the following is a linear equation in one variable?

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Category: Difference between expressions and equations

12. Which of the following is an equation?

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Category: Difference between expressions and equations

13. (A) The expression $3x + 2y$ is a linear equation in one variable.
(R) A linear equation in one variable has the highest power of the variable as 1.

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Category: Difference between expressions and equations

14. Which of the following is a linear expression in one variable?

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Category: Difference between expressions and equations

15. Consider the expressions $4y - 7$ and $y^2 + 3$. Which of these can be used to form a linear equation in one variable?

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Category: Understanding variables and constants

16. In the equation $5x - 10 = 15$, what is the Left Hand Side (LHS)?

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Category: Understanding variables and constants

17. Which of the following is an equation?

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Category: Understanding variables and constants

18. Which of the following is a linear expression in one variable?

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Category: Understanding variables and constants

19. (A) The expression $3x + 5$ is a linear expression in one variable.
(R) A linear expression in one variable has the highest power of the variable equal to 1.

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Category: Understanding variables and constants

20. (A) The equation $3x + 5 = 2x + 10$ is a linear equation in one variable.
(R) Linear equations in one variable are those where the highest power of the variable is 1.

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Category: What makes an equation linear?

21. Which of the following is a linear equation in one variable?

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Category: What makes an equation linear?

22. Which of the following is a linear equation in one variable?

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Category: What makes an equation linear?

23. Which of the following expressions is linear?

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Category: What makes an equation linear?

24. Identify which of the following is a linear expression:

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Category: What makes an equation linear?

25. (A) The equation $3x + 5 = 2x - 1$ is a linear equation in one variable.
(R) A linear equation in one variable has the highest power of the variable as 1.

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Category: Solving Equations Having Variable on Both Sides

26. Solve the equation $\frac{2x + 3}{4} = \frac{x - 1}{2}$.

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Category: Solving Equations Having Variable on Both Sides

27. Solve the equation $3(x - 4) + 2 = 5x - 2(3x + 1)$.

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Category: Solving Equations Having Variable on Both Sides

28. Solve the equation $3x + 4 = 2x + 9$.

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Category: Solving Equations Having Variable on Both Sides

29. Solve the equation $\frac{4x - 3}{2} = \frac{3x + 1}{2}$.

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Category: Solving Equations Having Variable on Both Sides

30. Solve the equation $\frac{4x - 7}{3} = \frac{2x + 5}{2}$.

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Category: Concept of balancing equations

31. Solve the equation $\frac{4x + 6}{2} = \frac{2x + 8}{2}$.

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Category: Concept of balancing equations

32. Solve the equation $3x + 5 = 2x + 10$.

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Category: Concept of balancing equations

33. Solve the equation $5x - 7 = 3x + 5$.

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Category: Concept of balancing equations

34. Solve the equation $5x - 4 = 3x + 6$.

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Category: Concept of balancing equations

35. Solve the equation $4x - 7 = 3x + 5$.

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Category: Transposing terms

36. Solve the equation $3x + 4 = 2x - 5$.

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Category: Transposing terms

37. Solve the equation $4x + 6 = 2x + 12$.

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Category: Transposing terms

38. Determine the solution of the equation: $5x - 4 = 3x + 12$

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Category: Transposing terms

39. Find the value of $x$ in the equation: $\frac{4x + 6}{2} = \frac{2x - 8}{2}$

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Category: Transposing terms

40. (A) In the equation $3x + 4 = 2x - 1$, transposing $2x$ to the left side gives $x + 4 = -1$.
(R) Transposing a term involves moving it from one side of the equation to the other by changing its sign.

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Category: Solving basic equations

41. Solve for $x$ in the equation $5x - 9 = 3x + 11$.

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Category: Solving basic equations

42. (A) To solve the equation $3x + 4 = x + 10$, you must first subtract $x$ from both sides to isolate the variable.
(R) Subtracting $x$ from both sides of the equation ensures that the variable terms are consolidated on one side, simplifying the equation for further solving.

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Category: Solving basic equations

43. Solve the equation $5x + 3 = 2x + 15$.

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Category: Solving basic equations

44. Solve the equation $\frac{4x + 6}{2} = \frac{2x - 8}{2}$.

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Category: Solving basic equations

45. Solve for $x$ in the equation $3x + 5 = 2x - 7$.

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Category: Examples and solutions

46. Find the value of $x$ in the equation $\frac{4x + 6}{3} = \frac{2x - 4}{2}$.

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Category: Examples and solutions

47. Solve the equation $5x - 7 = 2x + 8$.

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Category: Examples and solutions

48. (A) The equation $3x - 5 = x + 7$ has a solution where $x = 6$.
(R) To solve the equation $3x - 5 = x + 7$, we subtract $x$ from both sides and then add $5$ to both sides to find $x = 6$.

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Category: Examples and solutions

49. Solve the equation $\frac{2x}{3} + \frac{1}{2} = \frac{x}{2} + \frac{5}{6}$.

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Category: Examples and solutions

50. Solve the equation $3x - 4 = 2x + 5$.

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Category: Reducing Equations to Simpler Form

51. (A) Multiplying both sides of the equation by the LCM of the denominators simplifies the equation.
(R) The LCM ensures that all terms in the equation have integer coefficients, making it easier to solve.

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Category: Reducing Equations to Simpler Form

52. Solve the equation: $\frac{5x - 3}{2} - \frac{2x + 1}{4} = \frac{3x - 7}{8}$

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Category: Reducing Equations to Simpler Form

53. Solve the equation $\frac{5x - 3}{2} - \frac{3x + 4}{4} = \frac{7}{2}$.

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Category: Reducing Equations to Simpler Form

54. Solve the equation $\frac{5x - 2}{3} + \frac{2x + 1}{6} = \frac{7}{2}$.

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Category: Reducing Equations to Simpler Form

55. Solve the equation $\frac{2x + 5}{3} - \frac{x - 2}{6} = 4$.

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Category: Simplification of complex equations

56. Solve the equation $\frac{4x - 3}{5} - 1 = \frac{2x + 1}{3}$.

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Category: Simplification of complex equations

57. (A) The equation $\frac{2x + 1}{3} = \frac{x - 2}{6}$ can be simplified by multiplying both sides by 6.
(R) Multiplying both sides of an equation by the LCM of the denominators helps in eliminating fractions.

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Category: Simplification of complex equations

58. Solve the equation $2x - 3(2x - 5) = 4(3x - 1) + 7$.

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Category: Simplification of complex equations

59. (A) The equation $\frac{7x - 3}{2} + \frac{1}{4} = \frac{2x + 5}{4}$ can be simplified to $14x - 6 + 1 = 2x + 5$.
(R) Multiplying both sides of the equation by 4 eliminates the denominators and simplifies the equation.

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Category: Simplification of complex equations

60. Solve the equation $\frac{2x + 1}{3} + \frac{3x - 1}{4} = \frac{5x - 2}{6}$.

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Category: Use of LCM to eliminate fractions

61. Solve the equation: $\frac{2x + 1}{3} + \frac{x - 2}{6} = \frac{3x - 1}{2}$

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Category: Use of LCM to eliminate fractions

62. (A) To solve the equation $\frac{3x + 2}{4} + \frac{x - 1}{2} = \frac{5x - 3}{6}$, multiplying both sides by the LCM of the denominators simplifies the equation.
(R) Multiplying both sides of an equation by the LCM of the denominators eliminates the fractions and reduces the equation to a simpler form.

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Category: Use of LCM to eliminate fractions

63. (A) To solve the equation $\frac{3x + 2}{4} - \frac{x - 1}{3} = 1$, we must multiply both sides by the LCM of the denominators, which is 12.
(R) Multiplying both sides of an equation by the LCM of the denominators eliminates fractions and simplifies the equation.

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Category: Use of LCM to eliminate fractions

64. Solve $\frac{3x - 1}{4} + 2 = \frac{x + 5}{2}$

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Category: Use of LCM to eliminate fractions

65. Solve the equation $\frac{2x + 3}{5} + \frac{3x - 4}{2} = \frac{7x}{10} - 1$.

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Category: Handling brackets and distributed terms

66. Solve the equation: $3(x - 4) + 2(2x + 5) = 7x - 1$

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Category: Handling brackets and distributed terms

67. Solve the equation: $4(3x - 2) - 2(5x - 1) = 8$

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Category: Handling brackets and distributed terms

68. Solve the equation: $\frac{3x - 4}{2} + \frac{5(2x + 1)}{3} = \frac{7x - 2}{6}$

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Category: Handling brackets and distributed terms

69. Solve the equation: $4x - 3(2x - 5) = 2(x - 4) + 7$

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Category: Handling brackets and distributed terms

70. Solve the equation $2(3y - 1) = y + 7$

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Category: Stepwise approach to solving equations

71. Solve the equation: $2(3x - 1) + 4 = 3(2x + 1) - 5$

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Category: Stepwise approach to solving equations

72. (A) The equation $\frac{3x + 2}{4} + \frac{1}{4} = \frac{x - 1}{4}$ can be simplified by multiplying both sides by 4.
(R) Multiplying both sides of an equation by the same number helps in eliminating the denominators.

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Category: Stepwise approach to solving equations

73. Solve the equation: $\frac{2x + 1}{3} + \frac{3x - 2}{4} = \frac{x + 5}{6}$

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Category: Stepwise approach to solving equations

74. Solve the equation $\frac{2x + 5}{3} = \frac{x + 1}{2}$.

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Category: Stepwise approach to solving equations

75. Solve the equation $\frac{3x + 2}{4} = \frac{x - 1}{2}$.

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Category: Applications of Linear Equations

76. (A) A father is three times as old as his son. After 15 years, he will be twice as old as his son.
(R) This problem can be solved using the linear equation $3x + 15 = 2(x + 15)$, where $x$ is the current age of the son.

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Category: Applications of Linear Equations

77. The perimeter of a rectangle is 50 meters. If the length is 5 meters more than twice the width, what is the width of the rectangle?

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Category: Applications of Linear Equations

78. A person has a total of \$200 in the form of \$10 and \$20 notes. If the number of \$20 notes is 5 more than the number of \$10 notes, how many \$10 notes does the person have?

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Category: Applications of Linear Equations

79. The sum of two numbers is 45, and their difference is 15. What are the two numbers?

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Category: Applications of Linear Equations

80. The perimeter of a rectangle is 60 cm. If the length is twice the width, what is the width of the rectangle?

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Category: Word problems on numbers

81. Three times a number decreased by 5 equals 16. What is the number?

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Category: Word problems on numbers

82. The sum of two numbers is 50. If one number is 10 more than the other, what is the larger number?

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Category: Word problems on numbers

83. (A) If the sum of two consecutive integers is 25, then the larger integer must be 13.
(R) The difference between two consecutive integers is always 1.

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Category: Word problems on numbers

84. (A) A number is 6 more than twice another number. If the sum of the two numbers is 24, then the larger number is 18.
(R) The solution to the system of equations $x = 2y + 6$ and $x + y = 24$ gives the value of the larger number as 18.

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Category: Age-related problems

85. A man is four times as old as his daughter. In six years, he will be only three times as old as her. What is the present age of the daughter?

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Category: Age-related problems

86. The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. What is the current age of the father?

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Category: Age-related problems

87. (A) If the age of a person is doubled, it will always be greater than their current age.
(R) Doubling a positive number always results in a larger number.

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Category: Age-related problems

88. Five years ago, the age of a father was three times the age of his son. After ten years, the father's age will be twice the son's age. What is the current age of the son?

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Category: Perimeter-based problems

89. (A) The perimeter of a rectangle is given by the formula $P = 2(l + w)$, where $l$ is the length and $w$ is the width.
(R) If the perimeter of a rectangle is known, it is always possible to determine the exact length and width of the rectangle.

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Category: Perimeter-based problems

90. A triangle has sides in the ratio 3:4:5. If its perimeter is 48 cm, what is the length of the longest side?

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Category: Perimeter-based problems

91. The perimeter of a square is equal to the perimeter of a rectangle with length 10 cm and width 6 cm. What is the side length of the square?

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Category: Perimeter-based problems

92. A square has a perimeter of 24 cm. What is the length of one side of the square?

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Category: Money and currency-related problems

93. A shopkeeper sells two types of pens: type A costs \$2 each and type B costs \$3 each. If a customer buys a total of 10 pens and spends \$24, how many pens of type A did the customer buy?

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Category: Money and currency-related problems

94. If 5 euros are equivalent to 6 dollars and 3 dollars are equivalent to 2 pounds, how many pounds are equivalent to 10 euros?

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Category: Money and currency-related problems

95. John has a total of \$50 in 5-dollar and 10-dollar bills. If the number of 5-dollar bills is twice the number of 10-dollar bills, how many 5-dollar bills does he have?

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Category: Money and currency-related problems

96. A person has a total of \$500 in \$20 and \$50 notes. If the number of \$20 notes is 5 more than twice the number of \$50 notes, how many \$50 notes does the person have?

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Category: Real-life applications of linear equations

97. The perimeter of a rectangle is 40 cm. If the length is 4 cm more than twice the width, what is the length of the rectangle?

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Category: Real-life applications of linear equations

98. The perimeter of a rectangle is 30 meters. If the length is twice the width, what is the width of the rectangle?

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Category: Real-life applications of linear equations

99. A shopkeeper sells a pen for \$5 and a notebook for \$10. If a customer buys 3 pens and 2 notebooks, what is the total cost?

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Category: Real-life applications of linear equations

100. A father is three times as old as his son. After 12 years, he will be twice as old as his son. What are their present ages?

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