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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 240 · 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 + 6 = 4m + 19. What is m?
  2. 2.Solve: y/4 + y/2 = 3. What is y?
  3. 3.Solve: t/4 + t/3 = 35. What is t?
  4. 4.Solve: 3(t − 4) = t + 24. What is t?
  5. 5.Solve: 5(p − 1) = p + 51. What is p?
  6. 6.Solve: t/4 + t/3 = 21. What is t?
  7. 7.Solve: 7p + 7 = 3p + 43. What is p?
  8. 8.Solve: n/4 + n/5 = 45. What is n?
  9. 9.Solve: n/2 + n/6 = 12. What is n?
  10. 10.A father is 42 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  11. 11.A father is 16 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  12. 12.The sum of four consecutive whole numbers is 186. What is the largest of them?
  13. 13.The sum of two consecutive whole numbers is 91. What is the smallest of them?
  14. 14.A father is 34 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  15. 15.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  16. 16.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?
  17. 17.Solve: x/5 + x/2 = 56. What is x?
  18. 18.A father is 24 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?
  19. 19.Solve: 4(t − 5) = 3t + 9. What is t?
  20. 20.Solve: x/3 + x/6 = 21. What is x?
  21. 21.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  22. 22.Solve: t/6 + t/2 = 4. What is t?
  23. 23.Solve: 3y + 1 = y + 31. What is y?
  24. 24.The sum of three consecutive whole numbers is 177. What is the smallest of them?
  25. 25.Solve: 3t + 9 = 2t + 14. What is t?
  26. 26.Solve: 4y + 16 = 2y + 24. What is y?
  27. 27.The length of a rectangle is 4 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
  28. 28.Solve: 5(m − 3) = m + 5. What is m?
  29. 29.Solve: 3(x − 5) = x + 25. What is x?
  30. 30.Solve: 6(y − 3) = 3y + 21. What is y?
  31. 31.The sum of four consecutive whole numbers is 102. What is the largest of them?
  32. 32.Solve: 7y + 13 = 2y + 28. What is y?
  33. 33.The length of a rectangle is 5 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  34. 34.The sum of four consecutive whole numbers is 214. What is the largest of them?
  35. 35.The sum of three consecutive whole numbers is 162. What is the smallest of them?
  36. 36.Solve: x/4 + x/2 = 15. What is x?
  37. 37.The sum of three consecutive whole numbers is 105. What is the smallest of them?
  38. 38.Solve: x/3 + x/4 = 21. What is x?
  39. 39.The sum of four consecutive whole numbers is 110. What is the smallest of them?
  40. 40.Solve: n/2 + n/4 = 9. What is n?

Answer key

  1. 13
  2. 4
  3. 60
  4. 18
  5. 14
  6. 36
  7. 9
  8. 100
  9. 18
  10. 7
  11. 9
  12. 48
  13. 45
  14. 10
  15. 17
  16. 7
  17. 80
  18. 4
  19. 29
  20. 42
  21. 19
  22. 6
  23. 15
  24. 58
  25. 5
  26. 4
  27. 2
  28. 5
  29. 20
  30. 13
  31. 27
  32. 3
  33. 30
  34. 55
  35. 53
  36. 20
  37. 34
  38. 36
  39. 26
  40. 12

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