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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 477 · 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 three consecutive whole numbers is 123. What is the smallest of them?
  2. 2.The sum of two consecutive whole numbers is 99. What is the smallest of them?
  3. 3.Solve: x/3 + x/2 = 40. What is x?
  4. 4.Solve: 5t + 15 = 4t + 23. What is t?
  5. 5.The sum of four consecutive whole numbers is 98. What is the smallest of them?
  6. 6.Solve: t/3 + t/2 = 30. What is t?
  7. 7.The sum of three consecutive whole numbers is 48. What is the largest of them?
  8. 8.The sum of two consecutive whole numbers is 37. What is the smallest of them?
  9. 9.Solve: 6(n − 1) = n + 19. What is n?
  10. 10.Solve: 4m + 8 = 2m + 32. What is m?
  11. 11.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  12. 12.A father is 18 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  13. 13.Solve: 4p + 12 = p + 18. What is p?
  14. 14.Solve: 6n + 5 = 5n + 16. What is n?
  15. 15.Solve: 5t + 14 = 3t + 38. What is t?
  16. 16.Solve: 3(n − 4) = 2n + 11. What is n?
  17. 17.Solve: y/3 + y/4 = 56. What is y?
  18. 18.The sum of three consecutive whole numbers is 162. What is the largest of them?
  19. 19.A father is 24 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?
  20. 20.Solve: 3(m − 4) = 2m + 10. What is m?
  21. 21.A father is 21 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?
  22. 22.The sum of three consecutive whole numbers is 69. What is the smallest of them?
  23. 23.The length of a rectangle is 14 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  24. 24.The length of a rectangle is 8 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  25. 25.Solve: 4(n − 3) = 2n + 2. What is n?
  26. 26.Solve: 4(t − 1) = t + 35. What is t?
  27. 27.Solve: 4(p − 4) = 3p + 13. What is p?
  28. 28.Solve: 6y + 12 = 2y + 68. What is y?
  29. 29.Solve: 4(y − 3) = y + 12. What is y?
  30. 30.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?
  31. 31.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  32. 32.Solve: 3(x − 1) = x + 3. What is x?
  33. 33.A father is 28 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  34. 34.Solve: 5y + 13 = y + 33. What is y?
  35. 35.Solve: x/5 + x/2 = 21. What is x?
  36. 36.Solve: n/6 + n/2 = 12. What is n?
  37. 37.Solve: 3(t − 1) = t + 13. What is t?
  38. 38.Solve: 5t + 1 = 2t + 4. What is t?
  39. 39.Solve: 3(n − 5) = 2n + 3. What is n?
  40. 40.The sum of two consecutive whole numbers is 103. What is the smallest of them?

Answer key

  1. 40
  2. 49
  3. 48
  4. 8
  5. 23
  6. 36
  7. 17
  8. 18
  9. 5
  10. 12
  11. 10
  12. 12
  13. 2
  14. 11
  15. 12
  16. 23
  17. 96
  18. 55
  19. 10
  20. 22
  21. 3
  22. 22
  23. 22
  24. 16
  25. 7
  26. 13
  27. 29
  28. 14
  29. 8
  30. 4
  31. 11
  32. 3
  33. 6
  34. 5
  35. 30
  36. 18
  37. 8
  38. 1
  39. 18
  40. 51

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