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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 840 · 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: 4(y − 2) = 3y + 7. What is y?
  2. 2.The length of a rectangle is 6 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  3. 3.Solve: 4y + 7 = 3y + 22. What is y?
  4. 4.The sum of three consecutive whole numbers is 36. What is the smallest of them?
  5. 5.The sum of three consecutive whole numbers is 30. What is the smallest of them?
  6. 6.A father is 11 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  7. 7.The sum of four consecutive whole numbers is 66. What is the largest of them?
  8. 8.Solve: 3y + 17 = 2y + 31. What is y?
  9. 9.Solve: y/3 + y/5 = 8. What is y?
  10. 10.A father is 22 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?
  11. 11.The sum of two consecutive whole numbers is 117. What is the smallest of them?
  12. 12.The sum of four consecutive whole numbers is 138. What is the largest of them?
  13. 13.The sum of two consecutive whole numbers is 89. What is the smallest of them?
  14. 14.A father is 18 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?
  15. 15.The length of a rectangle is 8 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  16. 16.Solve: 3(x − 3) = 2x + 8. What is x?
  17. 17.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?
  18. 18.Solve: 4(p − 5) = 3p + 9. What is p?
  19. 19.Solve: 3n + 14 = 2n + 19. What is n?
  20. 20.The sum of four consecutive whole numbers is 182. What is the smallest of them?
  21. 21.Solve: 5y + 12 = 3y + 40. What is y?
  22. 22.Solve: 3p + 19 = 2p + 21. What is p?
  23. 23.Solve: t/2 + t/6 = 28. What is t?
  24. 24.Solve: t/4 + t/5 = 18. What is t?
  25. 25.Solve: y/5 + y/4 = 18. What is y?
  26. 26.Solve: y/4 + y/6 = 35. What is y?
  27. 27.The length of a rectangle is 1 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  28. 28.The length of a rectangle is 11 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  29. 29.The sum of two consecutive whole numbers is 13. What is the largest of them?
  30. 30.Solve: t/6 + t/2 = 24. What is t?
  31. 31.Solve: t/4 + t/5 = 9. What is t?
  32. 32.Solve: 6(y − 3) = 3y + 36. What is y?
  33. 33.Solve: n/6 + n/3 = 3. What is n?
  34. 34.Solve: x/5 + x/2 = 28. What is x?
  35. 35.The length of a rectangle is 5 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  36. 36.Solve: 5(x − 4) = 4x + 3. What is x?
  37. 37.Solve: 8x + 6 = 4x + 26. What is x?
  38. 38.Solve: n/6 + n/5 = 66. What is n?
  39. 39.Solve: 4(y − 1) = 2y + 22. What is y?
  40. 40.Solve: 5(p − 2) = p + 18. What is p?

Answer key

  1. 15
  2. 12
  3. 15
  4. 11
  5. 9
  6. 9
  7. 18
  8. 14
  9. 15
  10. 5
  11. 58
  12. 36
  13. 44
  14. 3
  15. 23
  16. 17
  17. 5
  18. 29
  19. 5
  20. 44
  21. 14
  22. 2
  23. 42
  24. 40
  25. 40
  26. 84
  27. 27
  28. 10
  29. 7
  30. 36
  31. 20
  32. 18
  33. 6
  34. 40
  35. 29
  36. 23
  37. 5
  38. 180
  39. 13
  40. 7

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