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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 81 · 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: 3m + 16 = m + 28. What is m?
  2. 2.Solve: 6(m − 2) = m + 18. What is m?
  3. 3.Solve: x/3 + x/6 = 15. What is x?
  4. 4.The length of a rectangle is 1 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  5. 5.The sum of three consecutive whole numbers is 135. What is the largest of them?
  6. 6.Solve: 4(p − 1) = 2p + 14. What is p?
  7. 7.Solve: 5t + 7 = t + 23. What is t?
  8. 8.The length of a rectangle is 3 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  9. 9.The length of a rectangle is 14 cm more than its width. Its perimeter is 144 cm. What is its width (in cm)?
  10. 10.Solve: 6(n − 1) = n + 19. What is n?
  11. 11.Solve: 4m + 1 = 3m + 15. What is m?
  12. 12.Solve: t/6 + t/5 = 55. What is t?
  13. 13.Solve: 9x + 3 = 6x + 39. What is x?
  14. 14.The sum of three consecutive whole numbers is 63. What is the largest of them?
  15. 15.Solve: 3y + 10 = y + 18. What is y?
  16. 16.Solve: 9m + 8 = 5m + 48. What is m?
  17. 17.The length of a rectangle is 14 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  18. 18.Solve: 9m + 2 = m + 42. What is m?
  19. 19.The sum of four consecutive whole numbers is 34. What is the smallest of them?
  20. 20.The length of a rectangle is 9 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  21. 21.Solve: n/2 + n/3 = 30. What is n?
  22. 22.Solve: 9p + 5 = 6p + 14. What is p?
  23. 23.The sum of three consecutive whole numbers is 27. What is the largest of them?
  24. 24.The sum of four consecutive whole numbers is 26. What is the smallest of them?
  25. 25.A father is 11 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  26. 26.Solve: 3y + 3 = y + 29. What is y?
  27. 27.Solve: m/6 + m/4 = 15. What is m?
  28. 28.Solve: 7m + 3 = 5m + 27. What is m?
  29. 29.The sum of three consecutive whole numbers is 153. What is the largest of them?
  30. 30.A father is 21 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  31. 31.The sum of three consecutive whole numbers is 102. What is the largest of them?
  32. 32.A father is 14 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  33. 33.The sum of two consecutive whole numbers is 45. What is the smallest of them?
  34. 34.The sum of two consecutive whole numbers is 91. What is the smallest of them?
  35. 35.Solve: 6(t − 3) = 4t + 18. What is t?
  36. 36.The length of a rectangle is 5 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  37. 37.Solve: 5t + 14 = 3t + 30. What is t?
  38. 38.A father is 5 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  39. 39.Solve: 5(m − 2) = 2m + 5. What is m?
  40. 40.A father is 24 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?

Answer key

  1. 6
  2. 6
  3. 30
  4. 29
  5. 46
  6. 9
  7. 4
  8. 3
  9. 29
  10. 5
  11. 14
  12. 150
  13. 12
  14. 22
  15. 4
  16. 10
  17. 18
  18. 5
  19. 7
  20. 10
  21. 36
  22. 3
  23. 10
  24. 5
  25. 4
  26. 13
  27. 36
  28. 12
  29. 52
  30. 6
  31. 35
  32. 5
  33. 22
  34. 45
  35. 18
  36. 25
  37. 8
  38. 2
  39. 5
  40. 2

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