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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 849 · 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: 9x + 11 = 2x + 67. What is x?
  2. 2.The sum of four consecutive whole numbers is 122. What is the smallest of them?
  3. 3.The sum of three consecutive whole numbers is 108. What is the largest of them?
  4. 4.Solve: n/4 + n/5 = 27. What is n?
  5. 5.Solve: t/5 + t/3 = 64. What is t?
  6. 6.The length of a rectangle is 15 cm more than its width. Its perimeter is 142 cm. What is its width (in cm)?
  7. 7.The length of a rectangle is 2 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  8. 8.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  9. 9.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: 5(m − 3) = m + 37. What is m?
  11. 11.The sum of two consecutive whole numbers is 27. What is the smallest of them?
  12. 12.Solve: 6x + 14 = 2x + 30. What is x?
  13. 13.Solve: 3m + 7 = m + 25. What is m?
  14. 14.Solve: 6(t − 2) = t + 48. What is t?
  15. 15.The sum of three consecutive whole numbers is 168. What is the smallest of them?
  16. 16.The length of a rectangle is 9 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
  17. 17.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?
  18. 18.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: y/4 + y/5 = 9. What is y?
  20. 20.Solve: 6(p − 5) = p + 45. What is p?
  21. 21.Solve: 3(t − 5) = 2t + 6. What is t?
  22. 22.Solve: x/4 + x/2 = 24. What is x?
  23. 23.Solve: y/3 + y/6 = 12. What is y?
  24. 24.The length of a rectangle is 14 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  25. 25.Solve: 3(m − 5) = m + 19. What is m?
  26. 26.Solve: 8t + 12 = 5t + 30. What is t?
  27. 27.Solve: 3(y − 3) = y + 9. What is y?
  28. 28.Solve: 5(m − 5) = 4m + 1. What is m?
  29. 29.Solve: 3m + 10 = 2m + 21. What is m?
  30. 30.The length of a rectangle is 1 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  31. 31.Solve: 3(m − 2) = 2m + 8. What is m?
  32. 32.Solve: 8y + 5 = 5y + 8. What is y?
  33. 33.Solve: 9y + 4 = 3y + 82. What is y?
  34. 34.A father is 33 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?
  35. 35.Solve: y/5 + y/2 = 28. What is y?
  36. 36.Solve: 6(x − 2) = 5x + 1. What is x?
  37. 37.The sum of two consecutive whole numbers is 29. What is the largest of them?
  38. 38.The sum of two consecutive whole numbers is 81. What is the smallest of them?
  39. 39.Solve: 8n + 16 = n + 114. What is n?
  40. 40.Solve: 5x + 12 = 2x + 42. What is x?

Answer key

  1. 8
  2. 29
  3. 37
  4. 60
  5. 120
  6. 28
  7. 30
  8. 4
  9. 11
  10. 13
  11. 13
  12. 4
  13. 9
  14. 12
  15. 55
  16. 2
  17. 5
  18. 8
  19. 20
  20. 15
  21. 21
  22. 32
  23. 24
  24. 14
  25. 17
  26. 6
  27. 9
  28. 26
  29. 11
  30. 18
  31. 14
  32. 1
  33. 13
  34. 7
  35. 40
  36. 13
  37. 15
  38. 40
  39. 14
  40. 10

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