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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 491 · 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 142. What is the largest of them?
  2. 2.Solve: 3(y − 4) = 2y + 1. What is y?
  3. 3.Solve: 5(y − 5) = 2y + 29. What is y?
  4. 4.The sum of three consecutive whole numbers is 69. What is the smallest of them?
  5. 5.Solve: y/5 + y/4 = 36. What is y?
  6. 6.Solve: p/4 + p/5 = 54. What is p?
  7. 7.Solve: 5(t − 1) = 4t + 3. What is t?
  8. 8.Solve: 3(y − 1) = y + 21. What is y?
  9. 9.Solve: x/5 + x/2 = 49. What is x?
  10. 10.Solve: 9p + 5 = 6p + 17. What is p?
  11. 11.Solve: 5x + 3 = 3x + 25. What is x?
  12. 12.A father is 6 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?
  13. 13.The length of a rectangle is 5 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  14. 14.The length of a rectangle is 10 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  15. 15.The sum of four consecutive whole numbers is 50. What is the largest of them?
  16. 16.The sum of four consecutive whole numbers is 182. What is the smallest of them?
  17. 17.Solve: 5y + 11 = y + 43. What is y?
  18. 18.Solve: 7y + 20 = 4y + 56. What is y?
  19. 19.Solve: x/2 + x/3 = 35. What is x?
  20. 20.Solve: 6(p − 5) = p + 65. What is p?
  21. 21.Solve: 4(n − 1) = n + 17. What is n?
  22. 22.The length of a rectangle is 3 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  23. 23.Solve: x/4 + x/3 = 7. What is x?
  24. 24.Solve: 3t + 19 = 2t + 24. What is t?
  25. 25.Solve: 8n + 7 = n + 49. What is n?
  26. 26.Solve: 4x + 10 = 3x + 20. What is x?
  27. 27.A father is 13 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  28. 28.Solve: m/4 + m/6 = 5. What is m?
  29. 29.A father is 15 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  30. 30.A father is 27 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?
  31. 31.Solve: 4(t − 2) = 2t + 12. What is t?
  32. 32.Solve: 4x + 6 = 3x + 15. What is x?
  33. 33.The sum of four consecutive whole numbers is 210. What is the smallest of them?
  34. 34.Solve: 6(t − 5) = t + 45. What is t?
  35. 35.The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
  36. 36.The sum of two consecutive whole numbers is 83. What is the largest of them?
  37. 37.Solve: 3(t − 5) = t + 17. What is t?
  38. 38.The sum of four consecutive whole numbers is 34. What is the smallest of them?
  39. 39.Solve: t/5 + t/4 = 9. What is t?
  40. 40.Solve: n/3 + n/5 = 24. What is n?

Answer key

  1. 37
  2. 13
  3. 18
  4. 22
  5. 80
  6. 120
  7. 8
  8. 12
  9. 70
  10. 4
  11. 11
  12. 2
  13. 26
  14. 27
  15. 14
  16. 44
  17. 8
  18. 12
  19. 42
  20. 19
  21. 7
  22. 27
  23. 12
  24. 5
  25. 6
  26. 10
  27. 10
  28. 12
  29. 11
  30. 4
  31. 10
  32. 9
  33. 51
  34. 15
  35. 3
  36. 42
  37. 16
  38. 7
  39. 20
  40. 45

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