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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 375 · 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: 5y + 17 = y + 29. What is y?
  2. 2.Solve: x/6 + x/5 = 22. What is x?
  3. 3.The sum of three consecutive whole numbers is 120. What is the smallest of them?
  4. 4.Solve: 5p + 19 = p + 75. What is p?
  5. 5.Solve: 4(p − 2) = p + 7. What is p?
  6. 6.The sum of four consecutive whole numbers is 42. What is the largest of them?
  7. 7.The sum of four consecutive whole numbers is 82. What is the largest of them?
  8. 8.The sum of two consecutive whole numbers is 53. What is the largest of them?
  9. 9.Solve: 3(y − 1) = 2y + 3. What is y?
  10. 10.Solve: t/2 + t/4 = 21. What is t?
  11. 11.Solve: 5y + 10 = 4y + 22. What is y?
  12. 12.The length of a rectangle is 13 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  13. 13.A father is 36 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  14. 14.Solve: 4y + 16 = y + 40. What is y?
  15. 15.Solve: 3x + 18 = 2x + 24. What is x?
  16. 16.Solve: 3n + 2 = n + 4. What is n?
  17. 17.A father is 7 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  18. 18.A father is 13 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  19. 19.The sum of two consecutive whole numbers is 21. What is the smallest of them?
  20. 20.Solve: 6m + 17 = 4m + 23. What is m?
  21. 21.Solve: 4(t − 3) = t + 15. What is t?
  22. 22.Solve: 3y + 11 = 2y + 24. What is y?
  23. 23.Solve: n/5 + n/3 = 16. What is n?
  24. 24.Solve: y/2 + y/4 = 15. What is y?
  25. 25.Solve: 4(y − 2) = y + 4. What is y?
  26. 26.Solve: 8t + 4 = t + 25. What is t?
  27. 27.The length of a rectangle is 6 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
  28. 28.Solve: 4(p − 4) = 3p + 1. What is p?
  29. 29.Solve: p/6 + p/2 = 28. What is p?
  30. 30.A father is 42 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  31. 31.Solve: 6m + 2 = 5m + 3. What is m?
  32. 32.The length of a rectangle is 6 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  33. 33.The sum of two consecutive whole numbers is 73. What is the smallest of them?
  34. 34.The sum of three consecutive whole numbers is 177. What is the largest of them?
  35. 35.Solve: 9p + 8 = 6p + 50. What is p?
  36. 36.The sum of four consecutive whole numbers is 58. What is the smallest of them?
  37. 37.Solve: m/4 + m/6 = 5. What is m?
  38. 38.The sum of four consecutive whole numbers is 134. What is the smallest of them?
  39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  40. 40.The length of a rectangle is 7 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?

Answer key

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

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