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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 988 · 40 sums
TalentJR

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.The sum of four consecutive whole numbers is 246. What is the smallest of them?
  2. 2.The sum of three consecutive whole numbers is 174. What is the smallest of them?
  3. 3.A father is 33 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  4. 4.Solve: 4(t − 1) = 2t + 4. What is t?
  5. 5.The length of a rectangle is 3 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  6. 6.Solve: 3(x − 1) = x + 3. What is x?
  7. 7.The length of a rectangle is 9 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  8. 8.Solve: 6(p − 2) = 5p + 7. What is p?
  9. 9.The sum of two consecutive whole numbers is 17. What is the largest of them?
  10. 10.The sum of two consecutive whole numbers is 63. What is the smallest of them?
  11. 11.Solve: y/3 + y/5 = 56. What is y?
  12. 12.Solve: 5(n − 2) = 4n + 5. What is n?
  13. 13.A father is 32 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  14. 14.Solve: p/6 + p/3 = 12. What is p?
  15. 15.Solve: 7y + 9 = 2y + 44. What is y?
  16. 16.The sum of two consecutive whole numbers is 107. What is the largest of them?
  17. 17.Solve: t/2 + t/6 = 4. What is t?
  18. 18.Solve: 6p + 6 = 3p + 9. What is p?
  19. 19.Solve: n/6 + n/4 = 15. What is n?
  20. 20.Solve: 8m + 5 = 3m + 10. What is m?
  21. 21.Solve: 4t + 13 = t + 58. What is t?
  22. 22.A father is 42 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  23. 23.Solve: 3x + 16 = 2x + 27. What is x?
  24. 24.The sum of two consecutive whole numbers is 59. What is the smallest of them?
  25. 25.Solve: 4(t − 4) = t + 26. What is t?
  26. 26.Solve: 3n + 4 = n + 14. What is n?
  27. 27.Solve: 3(t − 4) = t + 4. What is t?
  28. 28.Solve: 6(m − 1) = 4m + 6. What is m?
  29. 29.A father is 14 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  30. 30.The length of a rectangle is 3 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  31. 31.Solve: 6(t − 5) = 2t + 38. What is t?
  32. 32.The length of a rectangle is 15 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  33. 33.The sum of two consecutive whole numbers is 89. What is the smallest of them?
  34. 34.The sum of four consecutive whole numbers is 74. What is the smallest of them?
  35. 35.The sum of four consecutive whole numbers is 214. What is the smallest of them?
  36. 36.The length of a rectangle is 13 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  37. 37.The sum of two consecutive whole numbers is 67. What is the smallest of them?
  38. 38.Solve: 8p + 20 = 5p + 41. What is p?
  39. 39.The length of a rectangle is 11 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  40. 40.Solve: 3(p − 3) = p + 5. What is p?

Answer key

  1. 60
  2. 57
  3. 6
  4. 4
  5. 10
  6. 3
  7. 8
  8. 19
  9. 9
  10. 31
  11. 105
  12. 15
  13. 10
  14. 24
  15. 7
  16. 54
  17. 6
  18. 1
  19. 36
  20. 1
  21. 15
  22. 10
  23. 11
  24. 29
  25. 14
  26. 5
  27. 8
  28. 6
  29. 9
  30. 11
  31. 17
  32. 5
  33. 44
  34. 17
  35. 52
  36. 18
  37. 33
  38. 7
  39. 13
  40. 7

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