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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 45 · 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: 3(y − 1) = y + 9. What is y?
  2. 2.A father is 9 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?
  3. 3.Solve: 8n + 6 = n + 76. What is n?
  4. 4.Solve: 6(p − 2) = 2p + 24. What is p?
  5. 5.The sum of three consecutive whole numbers is 132. What is the smallest of them?
  6. 6.A father is 39 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?
  7. 7.Solve: x/2 + x/4 = 18. What is x?
  8. 8.The length of a rectangle is 14 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
  9. 9.A father is 39 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  10. 10.The sum of three consecutive whole numbers is 123. What is the smallest of them?
  11. 11.A father is 15 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?
  12. 12.Solve: 5(y − 1) = 3y + 3. What is y?
  13. 13.Solve: p/6 + p/4 = 5. What is p?
  14. 14.The sum of two consecutive whole numbers is 85. What is the smallest of them?
  15. 15.The length of a rectangle is 14 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  16. 16.The sum of three consecutive whole numbers is 81. What is the smallest of them?
  17. 17.The length of a rectangle is 11 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  18. 18.The length of a rectangle is 13 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  19. 19.The length of a rectangle is 6 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  20. 20.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  21. 21.Solve: 5(x − 5) = 4x + 2. What is x?
  22. 22.Solve: 4m + 11 = m + 41. What is m?
  23. 23.Solve: 5(x − 1) = 2x + 37. What is x?
  24. 24.Solve: p/6 + p/5 = 44. What is p?
  25. 25.Solve: 4(p − 4) = 2p + 14. What is p?
  26. 26.The sum of three consecutive whole numbers is 180. What is the largest of them?
  27. 27.Solve: p/4 + p/2 = 21. What is p?
  28. 28.The length of a rectangle is 5 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  29. 29.Solve: 4(p − 1) = 2p + 16. What is p?
  30. 30.Solve: x/5 + x/4 = 18. What is x?
  31. 31.Solve: m/3 + m/6 = 3. What is m?
  32. 32.Solve: 9y + 4 = 6y + 10. What is y?
  33. 33.The sum of two consecutive whole numbers is 91. What is the smallest of them?
  34. 34.The sum of four consecutive whole numbers is 70. What is the smallest of them?
  35. 35.Solve: 5(m − 5) = 4m + 11. What is m?
  36. 36.Solve: 7y + 5 = 3y + 25. What is y?
  37. 37.Solve: 6(n − 3) = 5n + 12. What is n?
  38. 38.Solve: 3(t − 1) = 2t + 2. What is t?
  39. 39.A father is 16 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  40. 40.Solve: 3(m − 1) = 2m + 8. What is m?

Answer key

  1. 6
  2. 2
  3. 10
  4. 9
  5. 43
  6. 10
  7. 24
  8. 28
  9. 6
  10. 40
  11. 4
  12. 4
  13. 12
  14. 42
  15. 21
  16. 26
  17. 13
  18. 18
  19. 19
  20. 5
  21. 27
  22. 10
  23. 14
  24. 120
  25. 15
  26. 61
  27. 28
  28. 12
  29. 10
  30. 40
  31. 6
  32. 2
  33. 45
  34. 16
  35. 36
  36. 5
  37. 30
  38. 5
  39. 12
  40. 11

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