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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 676 · 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: 6(t − 2) = 2t + 28. What is t?
  2. 2.The length of a rectangle is 3 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  3. 3.A father is 21 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?
  4. 4.The length of a rectangle is 1 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  5. 5.Solve: y/3 + y/2 = 40. What is y?
  6. 6.Solve: 6(x − 3) = 5x + 1. What is x?
  7. 7.The sum of four consecutive whole numbers is 70. What is the smallest of them?
  8. 8.The sum of three consecutive whole numbers is 54. What is the smallest of them?
  9. 9.Solve: n/2 + n/4 = 15. What is n?
  10. 10.The sum of two consecutive whole numbers is 105. What is the smallest of them?
  11. 11.The length of a rectangle is 1 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  12. 12.Solve: 6y + 16 = 5y + 30. What is y?
  13. 13.The sum of two consecutive whole numbers is 117. What is the largest of them?
  14. 14.A father is 12 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  15. 15.The length of a rectangle is 6 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  16. 16.Solve: p/5 + p/2 = 56. What is p?
  17. 17.Solve: 3(t − 1) = t + 21. What is t?
  18. 18.The length of a rectangle is 1 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  19. 19.Solve: 4(t − 3) = t + 12. What is t?
  20. 20.Solve: t/3 + t/4 = 28. What is t?
  21. 21.The sum of four consecutive whole numbers is 130. What is the smallest of them?
  22. 22.Solve: p/3 + p/6 = 21. What is p?
  23. 23.The length of a rectangle is 6 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  24. 24.A father is 27 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?
  25. 25.Solve: 5x + 14 = x + 34. What is x?
  26. 26.The sum of two consecutive whole numbers is 75. What is the largest of them?
  27. 27.The sum of two consecutive whole numbers is 37. What is the smallest of them?
  28. 28.The sum of three consecutive whole numbers is 66. What is the smallest of them?
  29. 29.The sum of four consecutive whole numbers is 54. What is the largest of them?
  30. 30.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?
  31. 31.A father is 54 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?
  32. 32.A father is 6 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  33. 33.A father is 30 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  34. 34.The length of a rectangle is 7 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  35. 35.Solve: 3m + 13 = m + 27. What is m?
  36. 36.The sum of three consecutive whole numbers is 138. What is the smallest of them?
  37. 37.The length of a rectangle is 11 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 9 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  39. 39.Solve: x/2 + x/3 = 10. What is x?
  40. 40.Solve: 3n + 11 = 2n + 21. What is n?

Answer key

  1. 10
  2. 8
  3. 5
  4. 25
  5. 48
  6. 19
  7. 16
  8. 17
  9. 20
  10. 52
  11. 15
  12. 14
  13. 59
  14. 4
  15. 9
  16. 80
  17. 12
  18. 11
  19. 8
  20. 48
  21. 31
  22. 42
  23. 23
  24. 2
  25. 5
  26. 38
  27. 18
  28. 21
  29. 15
  30. 5
  31. 11
  32. 5
  33. 4
  34. 24
  35. 7
  36. 45
  37. 21
  38. 27
  39. 12
  40. 10

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