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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 572 · 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 26 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  2. 2.Solve: 3m + 17 = m + 27. What is m?
  3. 3.Solve: 3(n − 1) = 2n + 12. What is n?
  4. 4.Solve: 5(t − 1) = t + 51. What is t?
  5. 5.A father is 36 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?
  6. 6.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  7. 7.Solve: 6(y − 5) = 3y + 30. What is y?
  8. 8.Solve: 5y + 9 = y + 17. What is y?
  9. 9.The length of a rectangle is 7 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  10. 10.Solve: 4(p − 3) = p + 27. What is p?
  11. 11.The sum of two consecutive whole numbers is 41. What is the largest of them?
  12. 12.The sum of three consecutive whole numbers is 126. What is the largest of them?
  13. 13.Solve: 7n + 7 = 5n + 37. What is n?
  14. 14.Solve: 3(t − 1) = t + 17. What is t?
  15. 15.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  16. 16.The length of a rectangle is 4 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  17. 17.The sum of four consecutive whole numbers is 54. What is the smallest of them?
  18. 18.The sum of two consecutive whole numbers is 119. What is the smallest of them?
  19. 19.Solve: 3(y − 5) = y + 23. What is y?
  20. 20.Solve: 8t + 8 = 4t + 32. What is t?
  21. 21.Solve: 4x + 9 = x + 24. What is x?
  22. 22.The sum of four consecutive whole numbers is 158. What is the largest of them?
  23. 23.Solve: 4(t − 3) = 2t + 14. What is t?
  24. 24.Solve: 6(y − 4) = y + 11. What is y?
  25. 25.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  26. 26.Solve: t/6 + t/4 = 25. What is t?
  27. 27.Solve: t/3 + t/6 = 24. What is t?
  28. 28.Solve: 4(p − 3) = 3p + 11. What is p?
  29. 29.A father is 6 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  30. 30.The length of a rectangle is 6 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  31. 31.Solve: 9p + 5 = p + 21. What is p?
  32. 32.Solve: t/6 + t/2 = 20. What is t?
  33. 33.The length of a rectangle is 11 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  34. 34.The length of a rectangle is 13 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  35. 35.Solve: 3(m − 4) = m + 8. What is m?
  36. 36.Solve: 5(t − 5) = 2t + 8. What is t?
  37. 37.The sum of four consecutive whole numbers is 46. What is the largest of them?
  38. 38.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  39. 39.Solve: 3(x − 4) = 2x + 3. What is x?
  40. 40.Solve: y/5 + y/4 = 72. What is y?

Answer key

  1. 12
  2. 5
  3. 15
  4. 14
  5. 12
  6. 8
  7. 20
  8. 2
  9. 15
  10. 13
  11. 21
  12. 43
  13. 15
  14. 10
  15. 7
  16. 27
  17. 12
  18. 59
  19. 19
  20. 6
  21. 5
  22. 41
  23. 13
  24. 7
  25. 17
  26. 60
  27. 48
  28. 23
  29. 2
  30. 16
  31. 2
  32. 30
  33. 11
  34. 23
  35. 10
  36. 11
  37. 13
  38. 29
  39. 15
  40. 160

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