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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 100 · 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(y − 2) = 4y + 10. What is y?
  2. 2.Solve: 8x + 12 = 7x + 13. What is x?
  3. 3.A father is 32 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?
  4. 4.The sum of three consecutive whole numbers is 45. What is the largest of them?
  5. 5.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  6. 6.Solve: 3(n − 2) = n + 4. What is n?
  7. 7.The sum of four consecutive whole numbers is 138. What is the smallest of them?
  8. 8.Solve: m/4 + m/6 = 20. What is m?
  9. 9.Solve: 9p + 5 = 5p + 37. What is p?
  10. 10.Solve: 6m + 13 = 4m + 29. What is m?
  11. 11.The sum of four consecutive whole numbers is 90. What is the largest of them?
  12. 12.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  13. 13.A father is 8 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  14. 14.The length of a rectangle is 6 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  15. 15.Solve: 5(x − 3) = 4x + 10. What is x?
  16. 16.Solve: 7y + 7 = 2y + 17. What is y?
  17. 17.Solve: 3(t − 5) = t + 7. What is t?
  18. 18.Solve: t/5 + t/4 = 54. What is t?
  19. 19.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  20. 20.Solve: 3(n − 3) = n + 23. What is n?
  21. 21.Solve: y/5 + y/6 = 66. What is y?
  22. 22.Solve: y/2 + y/6 = 28. What is y?
  23. 23.Solve: p/6 + p/2 = 20. What is p?
  24. 24.Solve: 6(p − 1) = 2p + 38. What is p?
  25. 25.Solve: t/2 + t/5 = 42. What is t?
  26. 26.Solve: 4y + 1 = y + 10. What is y?
  27. 27.Solve: 3(t − 1) = 2t + 12. What is t?
  28. 28.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  29. 29.A father is 16 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  30. 30.Solve: 5t + 18 = 2t + 21. What is t?
  31. 31.Solve: 3(t − 5) = 2t + 6. What is t?
  32. 32.The sum of three consecutive whole numbers is 138. What is the largest of them?
  33. 33.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?
  34. 34.A father is 12 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?
  35. 35.A father is 36 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?
  36. 36.The length of a rectangle is 7 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  37. 37.Solve: 4(m − 5) = 2m + 26. What is m?
  38. 38.Solve: n/6 + n/2 = 4. What is n?
  39. 39.Solve: t/2 + t/6 = 8. What is t?
  40. 40.Solve: 3(x − 2) = x + 8. What is x?

Answer key

  1. 11
  2. 1
  3. 12
  4. 16
  5. 11
  6. 5
  7. 33
  8. 48
  9. 8
  10. 8
  11. 24
  12. 9
  13. 3
  14. 26
  15. 25
  16. 2
  17. 11
  18. 120
  19. 8
  20. 16
  21. 180
  22. 42
  23. 30
  24. 11
  25. 60
  26. 3
  27. 15
  28. 10
  29. 8
  30. 1
  31. 21
  32. 47
  33. 5
  34. 2
  35. 5
  36. 19
  37. 23
  38. 6
  39. 12
  40. 7

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