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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 82 · 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(p − 1) = p + 3. What is p?
  2. 2.Solve: 5t + 2 = 2t + 29. What is t?
  3. 3.Solve: x/3 + x/5 = 24. What is x?
  4. 4.A father is 30 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  5. 5.Solve: m/2 + m/5 = 28. What is m?
  6. 6.The length of a rectangle is 12 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  7. 7.A father is 8 years older than his son. In 2 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 9 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  9. 9.The sum of four consecutive whole numbers is 166. What is the smallest of them?
  10. 10.Solve: 4x + 4 = x + 31. What is x?
  11. 11.Solve: 4(n − 1) = 3n + 7. What is n?
  12. 12.A father is 28 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  13. 13.Solve: 5(p − 2) = 3p + 14. What is p?
  14. 14.The length of a rectangle is 14 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  15. 15.Solve: t/5 + t/2 = 42. What is t?
  16. 16.The length of a rectangle is 12 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  17. 17.Solve: 5(p − 2) = 4p + 9. What is p?
  18. 18.The sum of three consecutive whole numbers is 144. What is the largest of them?
  19. 19.The length of a rectangle is 11 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  20. 20.Solve: 5(y − 5) = y + 23. What is y?
  21. 21.The sum of four consecutive whole numbers is 126. What is the largest of them?
  22. 22.Solve: 8y + 14 = y + 28. What is y?
  23. 23.Solve: 4y + 9 = 2y + 11. What is y?
  24. 24.Solve: y/6 + y/5 = 22. What is y?
  25. 25.The length of a rectangle is 13 cm more than its width. Its perimeter is 142 cm. What is its width (in cm)?
  26. 26.Solve: 4m + 5 = 2m + 27. What is m?
  27. 27.A father is 36 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?
  28. 28.Solve: 4(x − 5) = 3x + 2. What is x?
  29. 29.Solve: 4p + 12 = 2p + 28. What is p?
  30. 30.The sum of four consecutive whole numbers is 78. What is the largest of them?
  31. 31.Solve: 4t + 1 = 3t + 13. What is t?
  32. 32.The sum of four consecutive whole numbers is 62. What is the largest of them?
  33. 33.Solve: 3(n − 1) = 2n + 6. What is n?
  34. 34.Solve: 4(t − 2) = 3t + 3. What is t?
  35. 35.Solve: 6t + 3 = 5t + 12. What is t?
  36. 36.Solve: n/6 + n/3 = 6. What is n?
  37. 37.A father is 28 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  38. 38.Solve: 4(p − 2) = p + 19. What is p?
  39. 39.The sum of three consecutive whole numbers is 75. What is the smallest of them?
  40. 40.Solve: 4y + 11 = 3y + 22. What is y?

Answer key

  1. 3
  2. 9
  3. 45
  4. 2
  5. 40
  6. 6
  7. 2
  8. 18
  9. 40
  10. 9
  11. 11
  12. 12
  13. 12
  14. 13
  15. 60
  16. 23
  17. 19
  18. 49
  19. 3
  20. 12
  21. 33
  22. 2
  23. 1
  24. 60
  25. 29
  26. 11
  27. 11
  28. 22
  29. 8
  30. 21
  31. 12
  32. 17
  33. 9
  34. 11
  35. 9
  36. 12
  37. 10
  38. 9
  39. 24
  40. 11

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