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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 695 · 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 15 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  2. 2.Solve: 4n + 7 = 3n + 9. What is n?
  3. 3.Solve: x/6 + x/3 = 18. What is x?
  4. 4.Solve: 4(n − 4) = 2n + 2. What is n?
  5. 5.Solve: 6n + 15 = n + 40. What is n?
  6. 6.Solve: 6(y − 5) = y + 25. What is y?
  7. 7.Solve: m/6 + m/5 = 44. What is m?
  8. 8.Solve: 6(p − 5) = 2p + 10. What is p?
  9. 9.Solve: 7t + 10 = t + 76. What is t?
  10. 10.Solve: n/4 + n/2 = 6. What is n?
  11. 11.Solve: 3n + 11 = 2n + 12. What is n?
  12. 12.A father is 10 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  13. 13.Solve: t/3 + t/5 = 56. What is t?
  14. 14.The length of a rectangle is 15 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  15. 15.The sum of three consecutive whole numbers is 150. What is the largest of them?
  16. 16.Solve: 3p + 2 = 2p + 5. What is p?
  17. 17.Solve: 9n + 16 = 5n + 36. What is n?
  18. 18.A father is 11 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: 6(p − 5) = p + 50. What is p?
  20. 20.The length of a rectangle is 11 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  21. 21.The length of a rectangle is 12 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  22. 22.A father is 15 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  23. 23.A father is 51 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  24. 24.Solve: p/6 + p/4 = 15. What is p?
  25. 25.The length of a rectangle is 11 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  26. 26.The sum of four consecutive whole numbers is 174. What is the largest of them?
  27. 27.Solve: m/2 + m/4 = 9. What is m?
  28. 28.A father is 7 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  29. 29.Solve: x/4 + x/6 = 35. What is x?
  30. 30.Solve: n/4 + n/3 = 14. What is n?
  31. 31.The length of a rectangle is 2 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  32. 32.The sum of two consecutive whole numbers is 73. What is the largest of them?
  33. 33.The length of a rectangle is 8 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  34. 34.Solve: 4(p − 2) = p + 28. What is p?
  35. 35.Solve: 9t + 9 = 5t + 53. What is t?
  36. 36.Solve: p/3 + p/5 = 56. What is p?
  37. 37.The length of a rectangle is 9 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 3 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  39. 39.Solve: 6(y − 1) = 3y + 18. What is y?
  40. 40.Solve: 3(m − 3) = m + 13. What is m?

Answer key

  1. 6
  2. 2
  3. 36
  4. 9
  5. 5
  6. 11
  7. 120
  8. 10
  9. 11
  10. 8
  11. 1
  12. 4
  13. 105
  14. 3
  15. 51
  16. 3
  17. 5
  18. 8
  19. 16
  20. 4
  21. 16
  22. 3
  23. 10
  24. 36
  25. 24
  26. 45
  27. 12
  28. 3
  29. 84
  30. 24
  31. 15
  32. 37
  33. 8
  34. 12
  35. 11
  36. 105
  37. 13
  38. 10
  39. 8
  40. 11

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