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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 991 · 40 sums
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The method (Letters one side, numbers the other): Open brackets: a(x − b) = ax − ab. Fractions: multiply both sides by the LCM of the denominators — x/3 + x/4 = 14 → 4x + 3x = 168. Move letter terms to one side and numbers to the other (change the sign when a term crosses =), then divide. Word problems: consecutive numbers are n, n + 1, n + 2 …; ages in y years are age + y.

NameDateTime takenScore ___ / 40
  1. 1.Solve: p/2 + p/3 = 30. What is p?
  2. 2.Solve: n/3 + n/2 = 35. What is n?
  3. 3.Solve: 4(y − 5) = 2y + 2. What is y?
  4. 4.The sum of two consecutive whole numbers is 121. What is the largest of them?
  5. 5.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  6. 6.A father is 12 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  7. 7.Solve: 4n + 8 = 2n + 30. What is n?
  8. 8.Solve: 3(p − 2) = 2p + 9. What is p?
  9. 9.The length of a rectangle is 10 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  10. 10.The sum of four consecutive whole numbers is 238. What is the largest of them?
  11. 11.The sum of two consecutive whole numbers is 29. What is the smallest of them?
  12. 12.Solve: p/5 + p/2 = 14. What is p?
  13. 13.Solve: 6t + 4 = 3t + 34. What is t?
  14. 14.The length of a rectangle is 15 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  15. 15.The sum of four consecutive whole numbers is 126. What is the smallest of them?
  16. 16.The length of a rectangle is 6 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
  17. 17.Solve: 3(y − 4) = y + 16. What is y?
  18. 18.The length of a rectangle is 9 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  19. 19.Solve: t/4 + t/2 = 6. What is t?
  20. 20.Solve: 7x + 13 = x + 67. What is x?
  21. 21.Solve: 3(x − 5) = x + 7. What is x?
  22. 22.Solve: 4(n − 1) = 3n + 1. What is n?
  23. 23.Solve: 7t + 3 = 2t + 68. What is t?
  24. 24.A father is 36 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  25. 25.Solve: 7x + 17 = 2x + 22. What is x?
  26. 26.A father is 30 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  27. 27.Solve: 4x + 18 = x + 60. What is x?
  28. 28.Solve: 3(m − 1) = m + 21. What is m?
  29. 29.The length of a rectangle is 4 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  30. 30.The length of a rectangle is 1 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  31. 31.A father is 6 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  32. 32.The sum of four consecutive whole numbers is 126. What is the largest of them?
  33. 33.Solve: 8x + 1 = 5x + 25. What is x?
  34. 34.The sum of two consecutive whole numbers is 77. What is the smallest of them?
  35. 35.The sum of three consecutive whole numbers is 168. What is the largest of them?
  36. 36.Solve: 5(t − 3) = 4t + 10. What is t?
  37. 37.Solve: 3(y − 2) = 2y + 11. What is y?
  38. 38.Solve: x/4 + x/5 = 9. What is x?
  39. 39.The sum of two consecutive whole numbers is 61. What is the largest of them?
  40. 40.Solve: x/5 + x/6 = 11. What is x?

Answer key

  1. 36
  2. 42
  3. 11
  4. 61
  5. 2
  6. 2
  7. 11
  8. 15
  9. 27
  10. 61
  11. 14
  12. 20
  13. 10
  14. 26
  15. 30
  16. 5
  17. 14
  18. 17
  19. 8
  20. 9
  21. 11
  22. 5
  23. 13
  24. 4
  25. 1
  26. 12
  27. 14
  28. 12
  29. 5
  30. 14
  31. 2
  32. 33
  33. 8
  34. 38
  35. 57
  36. 25
  37. 17
  38. 20
  39. 31
  40. 30

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