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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 174 · 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: t/3 + t/6 = 18. What is t?
  2. 2.The sum of four consecutive whole numbers is 38. What is the smallest of them?
  3. 3.Solve: 3(t − 3) = 2t + 3. What is t?
  4. 4.A father is 12 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  5. 5.Solve: x/6 + x/5 = 22. What is x?
  6. 6.A father is 48 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  7. 7.Solve: p/3 + p/6 = 6. What is p?
  8. 8.Solve: x/3 + x/5 = 32. What is x?
  9. 9.Solve: 3(m − 2) = 2m + 4. What is m?
  10. 10.The length of a rectangle is 7 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  11. 11.The sum of two consecutive whole numbers is 59. What is the largest of them?
  12. 12.Solve: 3(t − 1) = t + 23. What is t?
  13. 13.Solve: 9x + 9 = 7x + 11. What is x?
  14. 14.The length of a rectangle is 4 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  15. 15.A father is 18 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?
  16. 16.Solve: 3x + 18 = x + 26. What is x?
  17. 17.Solve: 6(p − 5) = 4p + 10. What is p?
  18. 18.Solve: y/4 + y/2 = 21. What is y?
  19. 19.Solve: n/2 + n/5 = 7. What is n?
  20. 20.The sum of three consecutive whole numbers is 135. What is the smallest of them?
  21. 21.Solve: x/4 + x/5 = 27. What is x?
  22. 22.The sum of two consecutive whole numbers is 29. What is the largest of them?
  23. 23.Solve: 5(p − 5) = 2p + 38. What is p?
  24. 24.Solve: p/4 + p/2 = 9. What is p?
  25. 25.The length of a rectangle is 9 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  26. 26.The sum of three consecutive whole numbers is 84. What is the largest of them?
  27. 27.Solve: 4(n − 1) = 2n + 8. What is n?
  28. 28.A father is 33 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  29. 29.Solve: 6(m − 5) = 5m + 11. What is m?
  30. 30.A father is 16 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  31. 31.Solve: m/3 + m/6 = 21. What is m?
  32. 32.The length of a rectangle is 2 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  33. 33.Solve: 6n + 6 = n + 31. What is n?
  34. 34.The length of a rectangle is 10 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  35. 35.The sum of two consecutive whole numbers is 55. What is the smallest of them?
  36. 36.Solve: 4(p − 5) = 3p + 4. What is p?
  37. 37.The sum of two consecutive whole numbers is 15. What is the smallest of them?
  38. 38.The sum of two consecutive whole numbers is 49. What is the largest of them?
  39. 39.Solve: 6x + 7 = 5x + 19. What is x?
  40. 40.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?

Answer key

  1. 36
  2. 8
  3. 12
  4. 3
  5. 60
  6. 11
  7. 12
  8. 60
  9. 10
  10. 8
  11. 30
  12. 13
  13. 1
  14. 19
  15. 3
  16. 4
  17. 20
  18. 28
  19. 10
  20. 44
  21. 60
  22. 15
  23. 21
  24. 12
  25. 7
  26. 29
  27. 6
  28. 10
  29. 41
  30. 4
  31. 42
  32. 27
  33. 5
  34. 26
  35. 27
  36. 24
  37. 7
  38. 25
  39. 12
  40. 10

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