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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 424 · 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: 5y + 13 = 2y + 22. What is y?
  2. 2.The sum of four consecutive whole numbers is 186. What is the smallest of them?
  3. 3.Solve: 6m + 14 = m + 74. What is m?
  4. 4.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?
  5. 5.A father is 33 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?
  6. 6.The sum of three consecutive whole numbers is 21. What is the largest of them?
  7. 7.Solve: 6(x − 1) = x + 29. What is x?
  8. 8.The length of a rectangle is 14 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  9. 9.Solve: 5t + 4 = 4t + 16. What is t?
  10. 10.The length of a rectangle is 5 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  11. 11.Solve: y/2 + y/5 = 49. What is y?
  12. 12.Solve: 4(y − 1) = 3y + 12. What is y?
  13. 13.The sum of two consecutive whole numbers is 79. What is the smallest of them?
  14. 14.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  15. 15.Solve: 3(m − 4) = m + 6. What is m?
  16. 16.Solve: 7m + 6 = m + 96. What is m?
  17. 17.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  18. 18.Solve: 3(n − 1) = n + 9. What is n?
  19. 19.Solve: y/4 + y/2 = 18. What is y?
  20. 20.Solve: 5x + 5 = 2x + 44. What is x?
  21. 21.Solve: 6y + 2 = 3y + 8. What is y?
  22. 22.Solve: 5(x − 5) = 3x + 23. What is x?
  23. 23.Solve: 3(t − 1) = 2t + 11. What is t?
  24. 24.A father is 8 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  25. 25.The length of a rectangle is 10 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  26. 26.The sum of three consecutive whole numbers is 129. What is the smallest of them?
  27. 27.Solve: 5p + 7 = 4p + 17. What is p?
  28. 28.Solve: 3(n − 5) = n + 21. What is n?
  29. 29.The length of a rectangle is 3 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  30. 30.Solve: 4x + 19 = x + 64. What is x?
  31. 31.The sum of two consecutive whole numbers is 81. What is the smallest of them?
  32. 32.The sum of two consecutive whole numbers is 115. What is the smallest of them?
  33. 33.A father is 34 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  34. 34.Solve: p/4 + p/6 = 5. What is p?
  35. 35.The sum of two consecutive whole numbers is 59. What is the smallest of them?
  36. 36.The sum of two consecutive whole numbers is 65. What is the largest of them?
  37. 37.Solve: n/3 + n/6 = 3. What is n?
  38. 38.Solve: 4p + 3 = 2p + 29. What is p?
  39. 39.Solve: 5(x − 2) = 3x + 2. What is x?
  40. 40.The sum of four consecutive whole numbers is 198. What is the largest of them?

Answer key

  1. 3
  2. 45
  3. 12
  4. 11
  5. 4
  6. 8
  7. 7
  8. 6
  9. 12
  10. 30
  11. 70
  12. 16
  13. 39
  14. 4
  15. 9
  16. 15
  17. 12
  18. 6
  19. 24
  20. 13
  21. 2
  22. 24
  23. 14
  24. 6
  25. 25
  26. 42
  27. 10
  28. 18
  29. 19
  30. 15
  31. 40
  32. 57
  33. 9
  34. 12
  35. 29
  36. 33
  37. 6
  38. 13
  39. 6
  40. 51

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