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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 850 · 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: 3(n − 3) = 2n + 12. What is n?
  2. 2.A father is 16 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  3. 3.The sum of three consecutive whole numbers is 90. What is the largest of them?
  4. 4.The sum of four consecutive whole numbers is 166. What is the largest of them?
  5. 5.Solve: 6(t − 1) = 2t + 2. What is t?
  6. 6.The sum of two consecutive whole numbers is 15. What is the smallest of them?
  7. 7.The length of a rectangle is 9 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  8. 8.Solve: n/3 + n/6 = 18. What is n?
  9. 9.Solve: 6t + 9 = 4t + 35. What is t?
  10. 10.The length of a rectangle is 13 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  11. 11.Solve: t/4 + t/5 = 54. What is t?
  12. 12.Solve: 3(n − 2) = 2n + 8. What is n?
  13. 13.The sum of four consecutive whole numbers is 178. What is the largest of them?
  14. 14.Solve: 3(t − 3) = 2t + 5. What is t?
  15. 15.Solve: 6(p − 4) = p + 16. What is p?
  16. 16.The length of a rectangle is 4 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  17. 17.A father is 17 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  18. 18.The sum of two consecutive whole numbers is 25. What is the largest of them?
  19. 19.Solve: 4(t − 1) = 3t + 8. What is t?
  20. 20.Solve: 4(n − 3) = 3n + 9. What is n?
  21. 21.The length of a rectangle is 11 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  22. 22.Solve: 4m + 20 = 3m + 26. What is m?
  23. 23.Solve: 4(m − 1) = m + 5. What is m?
  24. 24.A father is 36 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?
  25. 25.The sum of four consecutive whole numbers is 102. What is the smallest of them?
  26. 26.Solve: 8y + 9 = y + 72. What is y?
  27. 27.The length of a rectangle is 3 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  28. 28.Solve: 4(p − 4) = 3p + 8. What is p?
  29. 29.Solve: 6(x − 4) = x + 61. What is x?
  30. 30.The sum of three consecutive whole numbers is 102. What is the smallest of them?
  31. 31.Solve: 5(m − 1) = m + 31. What is m?
  32. 32.Solve: 3x + 20 = x + 42. What is x?
  33. 33.A father is 39 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?
  34. 34.A father is 10 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  35. 35.Solve: 4t + 18 = 2t + 40. What is t?
  36. 36.Solve: x/5 + x/6 = 22. What is x?
  37. 37.Solve: 7x + 1 = 5x + 19. What is x?
  38. 38.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?
  39. 39.Solve: 8x + 16 = 2x + 82. What is x?
  40. 40.The sum of three consecutive whole numbers is 39. What is the largest of them?

Answer key

  1. 21
  2. 10
  3. 31
  4. 43
  5. 2
  6. 7
  7. 13
  8. 36
  9. 13
  10. 21
  11. 120
  12. 14
  13. 46
  14. 14
  15. 8
  16. 9
  17. 11
  18. 13
  19. 12
  20. 21
  21. 25
  22. 6
  23. 3
  24. 8
  25. 24
  26. 9
  27. 28
  28. 24
  29. 17
  30. 33
  31. 9
  32. 11
  33. 10
  34. 2
  35. 11
  36. 60
  37. 9
  38. 7
  39. 11
  40. 14

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