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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 388 · 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.The length of a rectangle is 2 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  2. 2.Solve: 4(m − 3) = m + 18. What is m?
  3. 3.Solve: 4n + 12 = 2n + 14. What is n?
  4. 4.Solve: 5(y − 4) = 3y + 4. What is y?
  5. 5.Solve: 3(n − 3) = n + 7. What is n?
  6. 6.Solve: 5m + 14 = m + 62. What is m?
  7. 7.The length of a rectangle is 14 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  8. 8.The sum of four consecutive whole numbers is 42. What is the smallest of them?
  9. 9.The length of a rectangle is 2 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  10. 10.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  11. 11.Solve: 6p + 14 = 2p + 70. What is p?
  12. 12.Solve: 6(x − 5) = 4x + 2. What is x?
  13. 13.A father is 14 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?
  14. 14.Solve: 4t + 16 = 2t + 34. What is t?
  15. 15.The length of a rectangle is 15 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  16. 16.Solve: x/4 + x/3 = 28. What is x?
  17. 17.Solve: 4(y − 2) = 3y + 13. What is y?
  18. 18.A father is 30 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  19. 19.Solve: 6(p − 5) = p + 5. What is p?
  20. 20.A father is 12 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  21. 21.Solve: 8p + 10 = 2p + 94. What is p?
  22. 22.The sum of two consecutive whole numbers is 75. What is the smallest of them?
  23. 23.Solve: y/3 + y/5 = 8. What is y?
  24. 24.The sum of four consecutive whole numbers is 74. What is the largest of them?
  25. 25.A father is 7 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  26. 26.The length of a rectangle is 9 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  27. 27.Solve: t/3 + t/4 = 35. What is t?
  28. 28.The sum of four consecutive whole numbers is 142. What is the largest of them?
  29. 29.The sum of two consecutive whole numbers is 17. What is the largest of them?
  30. 30.Solve: 5(x − 5) = 4x + 8. What is x?
  31. 31.The sum of two consecutive whole numbers is 29. What is the largest of them?
  32. 32.The length of a rectangle is 15 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  33. 33.Solve: 3(y − 2) = y + 2. What is y?
  34. 34.Solve: x/2 + x/6 = 16. What is x?
  35. 35.The sum of three consecutive whole numbers is 63. What is the smallest of them?
  36. 36.The sum of four consecutive whole numbers is 246. What is the largest of them?
  37. 37.Solve: 3(t − 5) = 2t + 12. What is t?
  38. 38.Solve: 3(t − 1) = 2t + 9. What is t?
  39. 39.Solve: 5(t − 1) = 2t + 34. What is t?
  40. 40.Solve: 3(y − 2) = y + 16. What is y?

Answer key

  1. 28
  2. 10
  3. 1
  4. 12
  5. 8
  6. 12
  7. 2
  8. 9
  9. 23
  10. 24
  11. 14
  12. 16
  13. 6
  14. 9
  15. 6
  16. 48
  17. 21
  18. 7
  19. 7
  20. 7
  21. 14
  22. 37
  23. 15
  24. 20
  25. 6
  26. 8
  27. 60
  28. 37
  29. 9
  30. 33
  31. 15
  32. 22
  33. 4
  34. 24
  35. 20
  36. 63
  37. 27
  38. 12
  39. 13
  40. 11

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