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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 289 · 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: n/3 + n/2 = 35. What is n?
  2. 2.The length of a rectangle is 1 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  3. 3.Solve: 5(m − 3) = 4m + 9. What is m?
  4. 4.Solve: p/6 + p/2 = 32. What is p?
  5. 5.Solve: 5p + 14 = p + 38. What is p?
  6. 6.The length of a rectangle is 15 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  7. 7.Solve: 3(y − 1) = 2y + 2. What is y?
  8. 8.Solve: p/3 + p/4 = 35. What is p?
  9. 9.A father is 18 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?
  10. 10.Solve: y/5 + y/4 = 27. What is y?
  11. 11.Solve: 3n + 1 = n + 5. What is n?
  12. 12.Solve: 7x + 3 = 2x + 23. What is x?
  13. 13.A father is 11 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  14. 14.Solve: 8n + 4 = 7n + 11. What is n?
  15. 15.Solve: 5(n − 2) = 2n + 29. What is n?
  16. 16.The length of a rectangle is 5 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  17. 17.The sum of two consecutive whole numbers is 47. What is the smallest of them?
  18. 18.The sum of two consecutive whole numbers is 77. What is the smallest of them?
  19. 19.Solve: p/5 + p/6 = 77. What is p?
  20. 20.Solve: 3(y − 2) = 2y + 9. What is y?
  21. 21.Solve: 4y + 6 = 3y + 18. What is y?
  22. 22.Solve: y/3 + y/5 = 24. What is y?
  23. 23.Solve: 4(m − 1) = m + 29. What is m?
  24. 24.The sum of four consecutive whole numbers is 230. What is the largest of them?
  25. 25.Solve: x/5 + x/6 = 11. What is x?
  26. 26.The length of a rectangle is 1 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  27. 27.The length of a rectangle is 3 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  28. 28.Solve: 3x + 6 = 2x + 17. What is x?
  29. 29.The sum of four consecutive whole numbers is 198. What is the smallest of them?
  30. 30.The sum of two consecutive whole numbers is 85. What is the largest of them?
  31. 31.The length of a rectangle is 4 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  32. 32.Solve: 7p + 16 = 5p + 34. What is p?
  33. 33.A father is 51 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?
  34. 34.A father is 36 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?
  35. 35.Solve: 3(t − 5) = t + 21. What is t?
  36. 36.Solve: 6x + 5 = 4x + 21. What is x?
  37. 37.A father is 10 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  38. 38.Solve: 4m + 8 = m + 23. What is m?
  39. 39.Solve: 6t + 16 = 2t + 68. What is t?
  40. 40.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?

Answer key

  1. 42
  2. 22
  3. 24
  4. 48
  5. 6
  6. 6
  7. 5
  8. 60
  9. 5
  10. 60
  11. 2
  12. 4
  13. 4
  14. 7
  15. 13
  16. 8
  17. 23
  18. 38
  19. 210
  20. 15
  21. 12
  22. 45
  23. 11
  24. 59
  25. 30
  26. 16
  27. 30
  28. 11
  29. 48
  30. 43
  31. 3
  32. 9
  33. 9
  34. 9
  35. 18
  36. 8
  37. 2
  38. 5
  39. 13
  40. 8

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