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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 87 · 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.Solve: 5m + 16 = 2m + 37. What is m?
  2. 2.Solve: 6t + 14 = 2t + 46. What is t?
  3. 3.The sum of two consecutive whole numbers is 83. What is the largest of them?
  4. 4.The sum of four consecutive whole numbers is 186. What is the largest of them?
  5. 5.A father is 54 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?
  6. 6.The sum of two consecutive whole numbers is 81. What is the smallest of them?
  7. 7.Solve: n/3 + n/4 = 28. What is n?
  8. 8.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  9. 9.Solve: 6(y − 3) = 3y + 6. What is y?
  10. 10.Solve: p/2 + p/3 = 5. What is p?
  11. 11.Solve: 3(x − 3) = 2x + 6. What is x?
  12. 12.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  13. 13.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  14. 14.The length of a rectangle is 12 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  15. 15.The sum of four consecutive whole numbers is 66. What is the smallest of them?
  16. 16.Solve: x/2 + x/3 = 10. What is x?
  17. 17.Solve: 7y + 10 = 3y + 30. What is y?
  18. 18.A father is 16 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: 4p + 1 = 2p + 29. What is p?
  20. 20.The length of a rectangle is 6 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  21. 21.Solve: x/2 + x/5 = 28. What is x?
  22. 22.A father is 10 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  23. 23.Solve: 5p + 10 = 4p + 12. What is p?
  24. 24.Solve: 6(x − 2) = 2x + 52. What is x?
  25. 25.Solve: p/2 + p/6 = 4. What is p?
  26. 26.Solve: 7n + 8 = 6n + 19. What is n?
  27. 27.Solve: 4(x − 5) = 3x + 10. What is x?
  28. 28.Solve: 6(t − 2) = 2t + 12. What is t?
  29. 29.A father is 21 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  30. 30.A father is 12 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  31. 31.Solve: 6(p − 3) = 5p + 13. What is p?
  32. 32.The length of a rectangle is 4 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  33. 33.The sum of two consecutive whole numbers is 31. What is the smallest of them?
  34. 34.Solve: 6n + 12 = 3n + 18. What is n?
  35. 35.Solve: m/2 + m/5 = 7. What is m?
  36. 36.Solve: 3(m − 5) = m + 15. What is m?
  37. 37.The sum of four consecutive whole numbers is 198. What is the largest of them?
  38. 38.The sum of four consecutive whole numbers is 226. What is the smallest of them?
  39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
  40. 40.Solve: t/6 + t/3 = 15. What is t?

Answer key

  1. 7
  2. 8
  3. 42
  4. 48
  5. 10
  6. 40
  7. 48
  8. 28
  9. 8
  10. 6
  11. 15
  12. 7
  13. 8
  14. 8
  15. 15
  16. 12
  17. 5
  18. 10
  19. 14
  20. 10
  21. 40
  22. 6
  23. 2
  24. 16
  25. 6
  26. 11
  27. 30
  28. 6
  29. 4
  30. 5
  31. 31
  32. 27
  33. 15
  34. 2
  35. 10
  36. 15
  37. 51
  38. 55
  39. 2
  40. 30

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