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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 20 · 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.The sum of two consecutive whole numbers is 41. What is the smallest of them?
  2. 2.Solve: 7y + 13 = 5y + 41. What is y?
  3. 3.Solve: 6(y − 1) = y + 64. What is y?
  4. 4.Solve: 3x + 16 = 2x + 17. What is x?
  5. 5.Solve: 3(t − 1) = t + 15. What is t?
  6. 6.Solve: 4t + 5 = 3t + 15. What is t?
  7. 7.A father is 4 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  8. 8.The sum of three consecutive whole numbers is 27. What is the smallest of them?
  9. 9.Solve: p/2 + p/5 = 42. What is p?
  10. 10.Solve: 4(x − 3) = x + 24. What is x?
  11. 11.Solve: 4(y − 3) = y + 12. What is y?
  12. 12.Solve: y/2 + y/5 = 14. What is y?
  13. 13.The length of a rectangle is 11 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  14. 14.Solve: 6t + 15 = 4t + 25. What is t?
  15. 15.Solve: 4t + 11 = 3t + 23. What is t?
  16. 16.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?
  17. 17.Solve: 4(m − 4) = 2m + 26. What is m?
  18. 18.Solve: m/6 + m/5 = 77. What is m?
  19. 19.Solve: 8p + 4 = 5p + 16. What is p?
  20. 20.Solve: 9m + 9 = m + 105. What is m?
  21. 21.The length of a rectangle is 15 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  22. 22.A father is 28 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  23. 23.The length of a rectangle is 12 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  24. 24.Solve: 6(y − 3) = 4y + 16. What is y?
  25. 25.The sum of four consecutive whole numbers is 82. What is the smallest of them?
  26. 26.The sum of three consecutive whole numbers is 144. What is the smallest of them?
  27. 27.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?
  28. 28.The sum of three consecutive whole numbers is 72. What is the largest of them?
  29. 29.The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  30. 30.The sum of two consecutive whole numbers is 95. What is the largest of them?
  31. 31.Solve: 4(n − 1) = 2n + 22. What is n?
  32. 32.A father is 24 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  33. 33.Solve: p/4 + p/3 = 49. What is p?
  34. 34.Solve: 3(n − 2) = 2n + 11. What is n?
  35. 35.The length of a rectangle is 1 cm more than its width. Its perimeter is 10 cm. What is its width (in cm)?
  36. 36.Solve: 3(p − 4) = p + 16. What is p?
  37. 37.Solve: 6(m − 4) = m + 1. What is m?
  38. 38.The sum of two consecutive whole numbers is 77. What is the largest of them?
  39. 39.The sum of four consecutive whole numbers is 58. What is the smallest of them?
  40. 40.Solve: 6(p − 1) = p + 14. What is p?

Answer key

  1. 20
  2. 14
  3. 14
  4. 1
  5. 9
  6. 10
  7. 3
  8. 8
  9. 60
  10. 12
  11. 8
  12. 20
  13. 15
  14. 5
  15. 12
  16. 5
  17. 21
  18. 210
  19. 4
  20. 12
  21. 6
  22. 7
  23. 5
  24. 17
  25. 19
  26. 47
  27. 11
  28. 25
  29. 20
  30. 48
  31. 13
  32. 10
  33. 84
  34. 17
  35. 2
  36. 14
  37. 5
  38. 39
  39. 13
  40. 4

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