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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 30 · 40 sums
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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: 4(y − 2) = y + 10. What is y?
  2. 2.Solve: n/3 + n/4 = 35. What is n?
  3. 3.Solve: y/6 + y/4 = 15. What is y?
  4. 4.A father is 27 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?
  5. 5.The length of a rectangle is 3 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  6. 6.Solve: 6t + 2 = 5t + 17. What is t?
  7. 7.Solve: 7n + 7 = 2n + 82. What is n?
  8. 8.The sum of two consecutive whole numbers is 73. What is the smallest of them?
  9. 9.Solve: 7t + 11 = 6t + 19. What is t?
  10. 10.Solve: 4n + 12 = n + 33. What is n?
  11. 11.Solve: 4(m − 3) = 2m + 12. What is m?
  12. 12.Solve: 5(t − 3) = t + 1. What is t?
  13. 13.Solve: 3m + 13 = m + 43. What is m?
  14. 14.The length of a rectangle is 6 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  15. 15.The sum of three consecutive whole numbers is 165. What is the smallest of them?
  16. 16.The length of a rectangle is 6 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  17. 17.Solve: 4p + 19 = 2p + 25. What is p?
  18. 18.Solve: 4(m − 3) = m + 21. What is m?
  19. 19.Solve: 6(x − 2) = x + 23. What is x?
  20. 20.Solve: 5x + 4 = 3x + 12. What is x?
  21. 21.Solve: 4(p − 1) = 3p + 3. What is p?
  22. 22.Solve: 5m + 13 = m + 65. What is m?
  23. 23.Solve: 3p + 6 = 2p + 7. What is p?
  24. 24.A father is 24 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?
  25. 25.A father is 36 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?
  26. 26.Solve: 5t + 6 = 4t + 16. What is t?
  27. 27.Solve: 3n + 1 = n + 5. What is n?
  28. 28.Solve: 3(m − 2) = m + 6. What is m?
  29. 29.Solve: x/4 + x/6 = 20. What is x?
  30. 30.The length of a rectangle is 2 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  31. 31.The sum of three consecutive whole numbers is 60. What is the largest of them?
  32. 32.The length of a rectangle is 10 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  33. 33.Solve: y/5 + y/2 = 28. What is y?
  34. 34.A father is 15 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  35. 35.A father is 16 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  36. 36.Solve: 6(y − 1) = 2y + 14. What is y?
  37. 37.The sum of three consecutive whole numbers is 96. What is the smallest of them?
  38. 38.Solve: m/5 + m/3 = 64. What is m?
  39. 39.Solve: 6(x − 3) = 3x + 3. What is x?
  40. 40.The sum of two consecutive whole numbers is 93. What is the smallest of them?

Answer key

  1. 6
  2. 60
  3. 36
  4. 2
  5. 26
  6. 15
  7. 15
  8. 36
  9. 8
  10. 7
  11. 12
  12. 4
  13. 15
  14. 7
  15. 54
  16. 8
  17. 3
  18. 11
  19. 7
  20. 4
  21. 7
  22. 13
  23. 1
  24. 6
  25. 10
  26. 10
  27. 2
  28. 6
  29. 48
  30. 14
  31. 21
  32. 20
  33. 40
  34. 10
  35. 2
  36. 5
  37. 31
  38. 120
  39. 7
  40. 46

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