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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 620 · 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: n/2 + n/4 = 6. What is n?
  2. 2.Solve: p/4 + p/3 = 21. What is p?
  3. 3.The sum of three consecutive whole numbers is 33. What is the largest of them?
  4. 4.Solve: 6(t − 3) = 5t + 4. What is t?
  5. 5.Solve: 3y + 12 = y + 28. What is y?
  6. 6.A father is 18 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?
  7. 7.A father is 32 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?
  8. 8.The length of a rectangle is 3 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  9. 9.Solve: 6(m − 1) = 3m + 18. What is m?
  10. 10.A father is 10 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  11. 11.Solve: 9n + 18 = 8n + 31. What is n?
  12. 12.Solve: m/3 + m/6 = 21. What is m?
  13. 13.Solve: x/2 + x/6 = 24. What is x?
  14. 14.A father is 12 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  15. 15.The sum of three consecutive whole numbers is 39. What is the largest of them?
  16. 16.Solve: 7p + 7 = 4p + 43. What is p?
  17. 17.Solve: 4t + 17 = 3t + 22. What is t?
  18. 18.Solve: 5(y − 5) = 2y + 26. What is y?
  19. 19.Solve: 9n + 9 = 2n + 65. What is n?
  20. 20.A father is 18 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?
  21. 21.The sum of three consecutive whole numbers is 150. What is the largest of them?
  22. 22.The sum of two consecutive whole numbers is 109. What is the largest of them?
  23. 23.Solve: t/6 + t/5 = 22. What is t?
  24. 24.Solve: 3(x − 1) = x + 13. What is x?
  25. 25.Solve: 8t + 13 = 4t + 65. What is t?
  26. 26.Solve: 6(n − 1) = n + 34. What is n?
  27. 27.A father is 45 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  28. 28.Solve: n/4 + n/6 = 35. What is n?
  29. 29.The sum of four consecutive whole numbers is 210. What is the smallest of them?
  30. 30.The sum of three consecutive whole numbers is 171. What is the smallest of them?
  31. 31.Solve: 6(t − 5) = 5t + 9. What is t?
  32. 32.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  33. 33.Solve: n/5 + n/3 = 8. What is n?
  34. 34.The length of a rectangle is 4 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  35. 35.The length of a rectangle is 10 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
  36. 36.The sum of three consecutive whole numbers is 96. What is the smallest of them?
  37. 37.The sum of three consecutive whole numbers is 120. What is the largest of them?
  38. 38.The length of a rectangle is 7 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  39. 39.Solve: 6(x − 5) = x + 60. What is x?
  40. 40.The sum of four consecutive whole numbers is 174. What is the largest of them?

Answer key

  1. 8
  2. 36
  3. 12
  4. 22
  5. 8
  6. 2
  7. 10
  8. 18
  9. 8
  10. 5
  11. 13
  12. 42
  13. 36
  14. 8
  15. 14
  16. 12
  17. 5
  18. 17
  19. 8
  20. 5
  21. 51
  22. 55
  23. 60
  24. 8
  25. 13
  26. 8
  27. 12
  28. 84
  29. 51
  30. 56
  31. 39
  32. 7
  33. 15
  34. 3
  35. 3
  36. 31
  37. 41
  38. 9
  39. 18
  40. 45

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