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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 230 · 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 5 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  2. 2.Solve: 3m + 17 = m + 25. What is m?
  3. 3.The length of a rectangle is 7 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  4. 4.Solve: 8x + 13 = 7x + 25. What is x?
  5. 5.A father is 16 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  6. 6.Solve: 6(n − 1) = 3n + 24. What is n?
  7. 7.Solve: 5t + 16 = t + 48. What is t?
  8. 8.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  9. 9.A father is 11 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: m/5 + m/2 = 28. What is m?
  11. 11.Solve: 5(m − 1) = 3m + 9. What is m?
  12. 12.A father is 42 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?
  13. 13.Solve: 4(t − 5) = t + 1. What is t?
  14. 14.The length of a rectangle is 6 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  15. 15.Solve: 3(x − 2) = 2x + 10. What is x?
  16. 16.Solve: x/3 + x/2 = 10. What is x?
  17. 17.Solve: 9y + 6 = 5y + 66. What is y?
  18. 18.The sum of four consecutive whole numbers is 114. What is the smallest of them?
  19. 19.The length of a rectangle is 14 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  20. 20.Solve: 8t + 6 = 2t + 60. What is t?
  21. 21.Solve: m/4 + m/5 = 54. What is m?
  22. 22.Solve: x/2 + x/3 = 20. What is x?
  23. 23.The length of a rectangle is 9 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
  24. 24.Solve: 9m + 17 = 7m + 45. What is m?
  25. 25.The length of a rectangle is 13 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  26. 26.Solve: y/4 + y/6 = 25. What is y?
  27. 27.Solve: 4m + 3 = m + 36. What is m?
  28. 28.Solve: 3t + 15 = 2t + 21. What is t?
  29. 29.The length of a rectangle is 15 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  30. 30.Solve: 7x + 17 = 2x + 42. What is x?
  31. 31.Solve: m/3 + m/4 = 42. What is m?
  32. 32.A father is 54 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?
  33. 33.Solve: 3t + 9 = t + 29. What is t?
  34. 34.Solve: m/4 + m/5 = 27. What is m?
  35. 35.Solve: 3(x − 3) = x + 1. What is x?
  36. 36.The sum of two consecutive whole numbers is 43. What is the largest of them?
  37. 37.The sum of two consecutive whole numbers is 85. What is the smallest of them?
  38. 38.The sum of three consecutive whole numbers is 171. What is the largest of them?
  39. 39.Solve: 7y + 8 = 4y + 35. What is y?
  40. 40.The length of a rectangle is 5 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?

Answer key

  1. 4
  2. 4
  3. 16
  4. 12
  5. 9
  6. 10
  7. 8
  8. 2
  9. 5
  10. 40
  11. 7
  12. 12
  13. 7
  14. 19
  15. 16
  16. 12
  17. 15
  18. 27
  19. 8
  20. 9
  21. 120
  22. 24
  23. 2
  24. 14
  25. 11
  26. 60
  27. 11
  28. 6
  29. 22
  30. 5
  31. 72
  32. 10
  33. 10
  34. 60
  35. 5
  36. 22
  37. 42
  38. 58
  39. 9
  40. 6

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