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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 470 · 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.The sum of two consecutive whole numbers is 83. What is the largest of them?
  2. 2.Solve: 6n + 12 = n + 22. What is n?
  3. 3.The sum of three consecutive whole numbers is 117. What is the smallest of them?
  4. 4.A father is 10 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  5. 5.Solve: x/5 + x/2 = 42. What is x?
  6. 6.Solve: 5(t − 1) = 3t + 11. What is t?
  7. 7.The length of a rectangle is 14 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  8. 8.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?
  9. 9.Solve: 4(n − 5) = 2n + 6. What is n?
  10. 10.Solve: 8p + 18 = 7p + 24. What is p?
  11. 11.Solve: 6x + 1 = 5x + 9. What is x?
  12. 12.Solve: x/2 + x/4 = 3. What is x?
  13. 13.Solve: 4p + 7 = p + 46. What is p?
  14. 14.Solve: 6y + 13 = 4y + 43. What is y?
  15. 15.Solve: t/6 + t/4 = 35. What is t?
  16. 16.Solve: 5x + 18 = 3x + 36. What is x?
  17. 17.Solve: 4(x − 1) = x + 32. What is x?
  18. 18.Solve: 7t + 1 = 4t + 25. What is t?
  19. 19.Solve: 4m + 5 = 3m + 16. What is m?
  20. 20.The sum of three consecutive whole numbers is 135. What is the largest of them?
  21. 21.Solve: 3y + 13 = 2y + 23. What is y?
  22. 22.The length of a rectangle is 12 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  23. 23.Solve: 3(y − 2) = 2y + 8. What is y?
  24. 24.A father is 45 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  25. 25.Solve: 9y + 11 = y + 19. What is y?
  26. 26.The sum of two consecutive whole numbers is 29. What is the smallest of them?
  27. 27.Solve: 9t + 3 = 6t + 39. What is t?
  28. 28.The length of a rectangle is 15 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  29. 29.Solve: 4(p − 3) = 3p + 10. What is p?
  30. 30.Solve: 7x + 6 = 6x + 18. What is x?
  31. 31.Solve: 3(x − 1) = x + 7. What is x?
  32. 32.Solve: 3(n − 4) = 2n + 8. What is n?
  33. 33.Solve: 3m + 14 = 2m + 18. What is m?
  34. 34.Solve: 7x + 1 = 5x + 11. What is x?
  35. 35.Solve: 3m + 11 = 2m + 17. What is m?
  36. 36.A father is 16 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?
  37. 37.The sum of three consecutive whole numbers is 108. What is the smallest of them?
  38. 38.The length of a rectangle is 6 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  39. 39.A father is 45 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  40. 40.Solve: 6(m − 2) = 5m + 1. What is m?

Answer key

  1. 42
  2. 2
  3. 38
  4. 3
  5. 60
  6. 8
  7. 24
  8. 5
  9. 13
  10. 6
  11. 8
  12. 4
  13. 13
  14. 15
  15. 84
  16. 9
  17. 12
  18. 8
  19. 11
  20. 46
  21. 10
  22. 8
  23. 14
  24. 10
  25. 1
  26. 14
  27. 12
  28. 23
  29. 22
  30. 12
  31. 5
  32. 20
  33. 4
  34. 5
  35. 6
  36. 4
  37. 35
  38. 24
  39. 7
  40. 13

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