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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 218 · 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: t/6 + t/3 = 15. What is t?
  2. 2.Solve: 3(y − 2) = 2y + 4. What is y?
  3. 3.Solve: 4(y − 4) = y + 14. What is y?
  4. 4.Solve: 4(t − 2) = t + 4. What is t?
  5. 5.Solve: 9n + 4 = 3n + 46. What is n?
  6. 6.Solve: 6(x − 2) = 2x + 36. What is x?
  7. 7.Solve: 6p + 7 = 5p + 15. What is p?
  8. 8.A father is 36 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  9. 9.The sum of four consecutive whole numbers is 46. What is the largest of them?
  10. 10.The sum of three consecutive whole numbers is 93. What is the largest of them?
  11. 11.The sum of two consecutive whole numbers is 15. What is the smallest of them?
  12. 12.Solve: y/2 + y/3 = 10. What is y?
  13. 13.Solve: m/3 + m/2 = 10. What is m?
  14. 14.The length of a rectangle is 14 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  15. 15.Solve: 4(n − 3) = 2n + 6. What is n?
  16. 16.A father is 15 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?
  17. 17.Solve: n/2 + n/3 = 5. What is n?
  18. 18.The length of a rectangle is 14 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  19. 19.The sum of three consecutive whole numbers is 144. What is the largest of them?
  20. 20.The sum of two consecutive whole numbers is 21. What is the smallest of them?
  21. 21.The length of a rectangle is 3 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  22. 22.The length of a rectangle is 1 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  23. 23.Solve: 9x + 4 = 4x + 34. What is x?
  24. 24.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  25. 25.The length of a rectangle is 5 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  26. 26.Solve: 5(y − 1) = y + 23. What is y?
  27. 27.Solve: y/3 + y/5 = 40. What is y?
  28. 28.A father is 45 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?
  29. 29.Solve: 7y + 14 = 5y + 26. What is y?
  30. 30.A father is 36 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?
  31. 31.Solve: 6(y − 2) = y + 48. What is y?
  32. 32.The length of a rectangle is 10 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 13. What is the smallest of them?
  34. 34.Solve: p/4 + p/2 = 18. What is p?
  35. 35.Solve: 3(n − 5) = n + 21. What is n?
  36. 36.The sum of two consecutive whole numbers is 39. What is the smallest of them?
  37. 37.Solve: 7m + 9 = 2m + 79. What is m?
  38. 38.Solve: 6m + 18 = m + 88. What is m?
  39. 39.The sum of three consecutive whole numbers is 141. What is the largest of them?
  40. 40.Solve: 4t + 10 = 2t + 22. What is t?

Answer key

  1. 30
  2. 10
  3. 10
  4. 4
  5. 7
  6. 12
  7. 8
  8. 9
  9. 13
  10. 32
  11. 7
  12. 12
  13. 12
  14. 6
  15. 9
  16. 3
  17. 6
  18. 21
  19. 49
  20. 10
  21. 9
  22. 23
  23. 6
  24. 17
  25. 25
  26. 7
  27. 75
  28. 11
  29. 6
  30. 10
  31. 12
  32. 16
  33. 6
  34. 24
  35. 18
  36. 19
  37. 14
  38. 14
  39. 48
  40. 6

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