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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 926 · 40 sums
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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: 7t + 14 = 5t + 32. What is t?
  2. 2.Solve: 6p + 15 = 3p + 48. What is p?
  3. 3.The length of a rectangle is 15 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  4. 4.Solve: 9m + 14 = 2m + 91. What is m?
  5. 5.Solve: 5(n − 3) = 4n + 3. What is n?
  6. 6.The sum of three consecutive whole numbers is 177. What is the largest of them?
  7. 7.Solve: n/3 + n/6 = 6. What is n?
  8. 8.Solve: 3p + 5 = p + 15. What is p?
  9. 9.Solve: 6t + 9 = 4t + 23. What is t?
  10. 10.Solve: 3(m − 2) = m + 16. What is m?
  11. 11.The length of a rectangle is 2 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  12. 12.Solve: 9x + 15 = 6x + 21. What is x?
  13. 13.Solve: 4x + 10 = 2x + 20. What is x?
  14. 14.The sum of two consecutive whole numbers is 113. What is the largest of them?
  15. 15.The sum of two consecutive whole numbers is 37. What is the largest of them?
  16. 16.Solve: 9x + 18 = 8x + 28. What is x?
  17. 17.The length of a rectangle is 9 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  18. 18.Solve: 9n + 17 = 7n + 43. What is n?
  19. 19.The sum of three consecutive whole numbers is 93. What is the largest of them?
  20. 20.Solve: n/4 + n/6 = 40. What is n?
  21. 21.The sum of four consecutive whole numbers is 54. What is the largest of them?
  22. 22.The sum of three consecutive whole numbers is 99. What is the largest of them?
  23. 23.The length of a rectangle is 10 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  24. 24.Solve: 3(n − 4) = n + 4. What is n?
  25. 25.Solve: 4(x − 2) = 2x + 26. What is x?
  26. 26.Solve: x/5 + x/6 = 55. What is x?
  27. 27.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  28. 28.The length of a rectangle is 4 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  29. 29.Solve: n/6 + n/2 = 8. What is n?
  30. 30.Solve: m/2 + m/4 = 9. What is m?
  31. 31.Solve: 7y + 20 = 6y + 21. What is y?
  32. 32.The sum of two consecutive whole numbers is 43. What is the largest of them?
  33. 33.Solve: 4(n − 2) = 2n + 8. What is n?
  34. 34.Solve: 4(y − 3) = 3y + 8. What is y?
  35. 35.A father is 51 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  36. 36.Solve: 6(p − 2) = 5p + 10. What is p?
  37. 37.Solve: 4(t − 2) = 2t + 8. What is t?
  38. 38.A father is 32 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?
  39. 39.The length of a rectangle is 4 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  40. 40.A father is 26 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?

Answer key

  1. 9
  2. 11
  3. 12
  4. 11
  5. 18
  6. 60
  7. 12
  8. 5
  9. 7
  10. 11
  11. 4
  12. 2
  13. 5
  14. 57
  15. 19
  16. 10
  17. 4
  18. 13
  19. 32
  20. 96
  21. 15
  22. 34
  23. 12
  24. 8
  25. 17
  26. 150
  27. 12
  28. 11
  29. 12
  30. 12
  31. 1
  32. 22
  33. 8
  34. 20
  35. 12
  36. 22
  37. 8
  38. 12
  39. 17
  40. 7

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