Linear equations in one variable in Mathematics

Updated on June 28, 2026 | By Learnzy Academy

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.

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List of question on "Linear equations in one variable"

  1. What is the solution to the equation 3x - 7 = 8?
  2. Solve: x/3 + x/4 - x/6 = 5.
  3. If x/a = b, then x = ab. This transformation uses which property?
  4. Solve: 15 - 3x = 6.
  5. If 3 pens cost Rs. 45, what is the cost of one pen?
  6. Solve: (2x - 1)/3 = 5.
  7. How many solutions does a linear equation in one variable typically have?
  8. Solve: 0.2x = 0.8.
  9. Solve: 6 + 2(y - 1) = 10.
  10. The difference between two numbers is 8. If the larger number is three times the smaller number, what is the smaller number?
  11. Which of the following is an example of an identity?
  12. Solve for k: 4k + 1 = 1.
  13. Solve: 5x - 7 - 2x = 8.
  14. A bag contains red and blue marbles. There are 3 times as many blue marbles as red marbles. If there are 28 marbles in total, how many red marbles are there?
  15. Solve: (x + 5)/(-2) = 3.
  16. What does 'isolate the variable' mean?
  17. Solve: 2.5x - 1 = 9.
  18. The statement "twice a number decreased by 5 is 11" can be written as:
  19. Solve: 2x/3 = 4/5.
  20. The sum of two consecutive odd numbers is 32. What is the larger number?
  21. Solve: 6x = -18.
  22. Solve: (x - 3)/4 = (x - 5)/2.
  23. What is the main goal when solving a linear equation?
  24. Solve: 5x = 25 - 5.
  25. Half of a number added to its one-third is 10. What is the number?
  26. Solve: 7 - 2x = x + 1.
  27. Which equation has x = 2 as its solution?
  28. A father is three times as old as his son. If the sum of their ages is 48, how old is the son?
  29. If x/4 = 3/2, what is x?
  30. Identify the property: a(b + c) = ab + ac
  31. Solve: (x + 1)/2 + (x - 1)/3 = 6.
  32. Solve: (x - 2)/3 = 4.
  33. John has Rs. 10 more than Mike. Together they have Rs. 60. How much money does Mike have?
  34. Solve: 2x + 4 = 2(x + 2).
  35. Solve: 3x + 5 = 3x + 10.
  36. Which of the following is NOT an inverse operation?
  37. When transposing a term, what happens?
  38. Solve: x/2 + 0.5 = 2.
  39. 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?
  40. Solve: -3(x + 2) = 9.
  41. To solve for x in the equation x/5 = 7, you would:
  42. Solve: (x/2) + 1 = (x/3) + 2.
  43. The sum of two consecutive even integers is 26. What are the integers?
  44. Which statement about linear equations in one variable is false?
  45. Solve: 5(y - 2) = 3y + 4.
  46. The solution of an equation is the value of the variable that:
  47. To solve 3x + 7 = 16, what is the first step?
  48. Sara is currently x years old. In 5 years, she will be 18. Which equation represents this?
  49. Solve: x/4 - x/8 = 1.
  50. Solve for p: p/7 + 2 = 5.
  51. In the equation -6x + 3 = 15, what is the coefficient of x?
  52. A rectangular garden has a perimeter of 40 meters. If the width is 8 meters, what is the length?
  53. Solve: 0.3x + 0.2 = 0.5x - 0.4.
  54. Which operation undoes addition?
  55. An equation is balanced when:
  56. When you 'solve' an equation, you are finding the:
  57. Solve: 4(x - 1) = -8.
  58. Solve for y: -2y - 5 = 7.
  59. The ratio of two numbers is 2:3. If their sum is 30, what is the larger number?
  60. Solve: (2x - 4)/2 = 6.
  61. Which of the following is NOT a linear equation in one variable?
  62. Solve: 7x - 4x + 2 = 11.
  63. Solve for n: 2n + 5 - 3 = 10.
  64. If five times a number minus 3 is 17, what is the number?
  65. Is x = -2 a solution to the equation 3x + 5 = -1?
  66. An equation where the highest power of the variable is one is called a:
  67. Solve: x/2 + x/3 = 10.
  68. The perimeter of a rectangle is 30 cm. If its length is 10 cm, what is its width?
  69. Solve: (x + 1)/2 = 5.
  70. Solve: 3(x - 2) = 2x + 1.
  71. Solve for x: 10 - x = 4.
  72. In the equation 5x + 8 = 23, what is the constant term on the left side?
  73. In the equation 7p - 2 = 12, what is the variable?
  74. To solve 3x = 15, what is the inverse operation for multiplication by 3?
  75. If x - 5 = 10, then adding 5 to both sides gives x = 15. What operation was used?
  76. If a = b, then a + c = b + c. This is an example of which property?
  77. Find the value of k: k + 1.2 = 3.5.
  78. Solve: 0.5x = 4.
  79. Rohan is 5 years older than his sister Priya. If the sum of their ages is 27, how old is Priya?
  80. The sum of two consecutive integers is 25. What is the smaller integer?
  81. Which of the following is true for a linear equation in one variable?
  82. Solve for z: z/5 - 2 = 0.
  83. What is the solution to x/3 + 1 = 4?
  84. Solve: 2(x + 3) = 10.
  85. Find the value of y: 4y - 6 = y + 3.
  86. Solve for a: 5a = 2a + 9.
  87. Simplify and solve: 2x + 3x = 25.
  88. Solve for m: -3m = 18.
  89. Solve for p: p - (-4) = 10.
  90. Three times a number is 27. What is the number?
  91. A number increased by 7 is 15. What is the number?
  92. Which value of x makes the equation 5x - 2 = 13 true?
  93. When 6 is transposed from the left side to the right side of the equation x + 6 = 10, what happens to its sign?
  94. Solve the equation 2x + 1 = 7.
  95. What is the solution to x/2 = 9?
  96. Find the value of y if 4y = 20.
  97. Solve for x: x - 3 = 8.
  98. If x + 5 = 12, what is the value of x?
  99. Which of the following is a linear equation in one variable?
  100. What is the degree of a linear equation in one variable?