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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 838 · 40 sums
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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 length of a rectangle is 10 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  2. 2.The length of a rectangle is 5 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  3. 3.The sum of four consecutive whole numbers is 138. What is the largest of them?
  4. 4.Solve: 3t + 11 = t + 39. What is t?
  5. 5.Solve: 4(n − 2) = n + 7. What is n?
  6. 6.A father is 12 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  7. 7.The sum of four consecutive whole numbers is 198. What is the smallest of them?
  8. 8.Solve: 6(y − 4) = 4y + 8. What is y?
  9. 9.Solve: y/6 + y/3 = 6. What is y?
  10. 10.Solve: 3p + 14 = p + 22. What is p?
  11. 11.The sum of two consecutive whole numbers is 79. What is the largest of them?
  12. 12.Solve: 4x + 13 = 2x + 31. What is x?
  13. 13.Solve: 4(y − 2) = 2y + 16. What is y?
  14. 14.The sum of four consecutive whole numbers is 210. What is the smallest of them?
  15. 15.Solve: y/3 + y/5 = 56. What is y?
  16. 16.Solve: 3n + 1 = n + 17. What is n?
  17. 17.Solve: 3m + 5 = 2m + 19. What is m?
  18. 18.The sum of four consecutive whole numbers is 62. What is the smallest of them?
  19. 19.Solve: t/3 + t/5 = 16. What is t?
  20. 20.A father is 32 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  21. 21.Solve: 6(x − 2) = x + 13. What is x?
  22. 22.Solve: 9y + 2 = 7y + 22. What is y?
  23. 23.The sum of three consecutive whole numbers is 45. What is the largest of them?
  24. 24.Solve: 3m + 3 = 2m + 13. What is m?
  25. 25.Solve: t/4 + t/2 = 3. What is t?
  26. 26.The length of a rectangle is 1 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  27. 27.Solve: m/3 + m/2 = 15. What is m?
  28. 28.A father is 3 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  29. 29.The sum of two consecutive whole numbers is 119. What is the smallest of them?
  30. 30.The sum of four consecutive whole numbers is 162. What is the smallest of them?
  31. 31.Solve: 6p + 19 = 2p + 23. What is p?
  32. 32.A father is 30 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  33. 33.Solve: 3m + 1 = m + 11. What is m?
  34. 34.The length of a rectangle is 2 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  35. 35.Solve: 3p + 1 = p + 15. What is p?
  36. 36.A father is 13 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  37. 37.The sum of four consecutive whole numbers is 70. What is the smallest of them?
  38. 38.The length of a rectangle is 14 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  39. 39.Solve: 3m + 11 = m + 13. What is m?
  40. 40.Solve: 3(m − 3) = 2m + 1. What is m?

Answer key

  1. 4
  2. 14
  3. 36
  4. 14
  5. 5
  6. 2
  7. 48
  8. 16
  9. 12
  10. 4
  11. 40
  12. 9
  13. 12
  14. 51
  15. 105
  16. 8
  17. 14
  18. 14
  19. 30
  20. 11
  21. 5
  22. 10
  23. 16
  24. 10
  25. 4
  26. 29
  27. 18
  28. 2
  29. 59
  30. 39
  31. 1
  32. 6
  33. 5
  34. 4
  35. 7
  36. 11
  37. 16
  38. 17
  39. 1
  40. 10

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