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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 686 · 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.A father is 18 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  2. 2.Solve: 3(y − 4) = y + 12. What is y?
  3. 3.Solve: x/4 + x/3 = 28. What is x?
  4. 4.Solve: 5t + 14 = t + 66. What is t?
  5. 5.Solve: 5m + 19 = m + 27. What is m?
  6. 6.The sum of three consecutive whole numbers is 147. What is the smallest of them?
  7. 7.The sum of four consecutive whole numbers is 94. What is the largest of them?
  8. 8.The sum of four consecutive whole numbers is 82. What is the largest of them?
  9. 9.The length of a rectangle is 8 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  10. 10.Solve: 4n + 11 = n + 41. What is n?
  11. 11.Solve: 6(t − 4) = 4t + 2. What is t?
  12. 12.The length of a rectangle is 6 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  13. 13.Solve: m/6 + m/3 = 18. What is m?
  14. 14.The length of a rectangle is 12 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  15. 15.The sum of four consecutive whole numbers is 110. What is the largest of them?
  16. 16.A father is 22 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  17. 17.A father is 16 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?
  18. 18.Solve: 6(n − 4) = 2n + 8. What is n?
  19. 19.The length of a rectangle is 13 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  20. 20.The sum of four consecutive whole numbers is 246. What is the smallest of them?
  21. 21.Solve: p/3 + p/2 = 5. What is p?
  22. 22.A father is 27 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?
  23. 23.A father is 24 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?
  24. 24.Solve: 6(m − 1) = 4m + 26. What is m?
  25. 25.The length of a rectangle is 14 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  26. 26.The length of a rectangle is 11 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  27. 27.The length of a rectangle is 15 cm more than its width. Its perimeter is 150 cm. What is its width (in cm)?
  28. 28.Solve: 6(m − 2) = 3m + 39. What is m?
  29. 29.Solve: 3(y − 4) = 2y + 2. What is y?
  30. 30.Solve: 6p + 7 = 2p + 63. What is p?
  31. 31.Solve: 6(n − 1) = n + 59. What is n?
  32. 32.The sum of four consecutive whole numbers is 82. What is the smallest of them?
  33. 33.A father is 30 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  34. 34.Solve: 3(m − 1) = 2m + 3. What is m?
  35. 35.The length of a rectangle is 7 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
  36. 36.The length of a rectangle is 5 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  37. 37.Solve: 3(m − 5) = m + 5. What is m?
  38. 38.The sum of four consecutive whole numbers is 142. What is the smallest of them?
  39. 39.Solve: 3t + 11 = 2t + 25. What is t?
  40. 40.A father is 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?

Answer key

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

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