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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 107 · 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 15 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  2. 2.Solve: 7x + 7 = 4x + 43. What is x?
  3. 3.Solve: 3m + 11 = 2m + 20. What is m?
  4. 4.A father is 16 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?
  5. 5.Solve: 6(n − 3) = 5n + 3. What is n?
  6. 6.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  7. 7.The sum of two consecutive whole numbers is 45. What is the smallest of them?
  8. 8.The sum of four consecutive whole numbers is 134. What is the smallest of them?
  9. 9.A father is 51 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?
  10. 10.The length of a rectangle is 6 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  11. 11.Solve: 3(m − 5) = 2m + 9. What is m?
  12. 12.The sum of three consecutive whole numbers is 51. What is the smallest of them?
  13. 13.The sum of three consecutive whole numbers is 24. What is the smallest of them?
  14. 14.Solve: 5x + 2 = 3x + 28. What is x?
  15. 15.Solve: 3(t − 4) = t + 22. What is t?
  16. 16.The sum of three consecutive whole numbers is 96. What is the smallest of them?
  17. 17.Solve: t/4 + t/5 = 63. What is t?
  18. 18.A father is 45 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?
  19. 19.Solve: 5(x − 1) = 4x + 10. What is x?
  20. 20.Solve: y/5 + y/3 = 16. What is y?
  21. 21.The length of a rectangle is 13 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  22. 22.Solve: 4(x − 1) = 2x + 20. What is x?
  23. 23.Solve: 6(t − 5) = t + 5. What is t?
  24. 24.The length of a rectangle is 1 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  25. 25.Solve: 4(x − 5) = 2x + 16. What is x?
  26. 26.Solve: x/4 + x/2 = 15. What is x?
  27. 27.Solve: 7p + 14 = 6p + 29. What is p?
  28. 28.The sum of two consecutive whole numbers is 43. What is the smallest of them?
  29. 29.Solve: 4(t − 2) = t + 19. What is t?
  30. 30.Solve: 4p + 10 = 3p + 18. What is p?
  31. 31.Solve: 5t + 6 = t + 58. What is t?
  32. 32.The length of a rectangle is 12 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  33. 33.Solve: 3(y − 2) = 2y + 8. What is y?
  34. 34.Solve: 3(y − 2) = y + 20. What is y?
  35. 35.Solve: 5p + 19 = 3p + 31. What is p?
  36. 36.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  37. 37.Solve: 9t + 10 = t + 66. What is t?
  38. 38.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?
  39. 39.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?
  40. 40.Solve: 4p + 4 = p + 13. What is p?

Answer key

  1. 11
  2. 12
  3. 9
  4. 5
  5. 21
  6. 28
  7. 22
  8. 32
  9. 9
  10. 29
  11. 24
  12. 16
  13. 7
  14. 13
  15. 17
  16. 31
  17. 140
  18. 8
  19. 15
  20. 30
  21. 21
  22. 12
  23. 7
  24. 28
  25. 18
  26. 20
  27. 15
  28. 21
  29. 9
  30. 8
  31. 13
  32. 23
  33. 14
  34. 13
  35. 6
  36. 29
  37. 7
  38. 5
  39. 5
  40. 3

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