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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 140 · 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: 5(p − 1) = 3p + 25. What is p?
  2. 2.Solve: 8n + 1 = 7n + 13. What is n?
  3. 3.Solve: 3x + 1 = x + 7. What is x?
  4. 4.Solve: 3t + 17 = 2t + 32. What is t?
  5. 5.The length of a rectangle is 12 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  6. 6.The length of a rectangle is 9 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  7. 7.A father is 10 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 14 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  9. 9.Solve: m/2 + m/5 = 42. What is m?
  10. 10.The sum of two consecutive whole numbers is 39. What is the smallest of them?
  11. 11.Solve: t/6 + t/3 = 21. What is t?
  12. 12.The sum of three consecutive whole numbers is 57. What is the largest of them?
  13. 13.Solve: x/3 + x/2 = 15. What is x?
  14. 14.Solve: 7n + 4 = 5n + 14. What is n?
  15. 15.The sum of three consecutive whole numbers is 96. What is the smallest of them?
  16. 16.The length of a rectangle is 13 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  17. 17.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  18. 18.The length of a rectangle is 1 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  19. 19.A father is 16 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  20. 20.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  21. 21.Solve: 4y + 18 = 3y + 27. What is y?
  22. 22.Solve: 6(n − 1) = 3n + 18. What is n?
  23. 23.Solve: 4(n − 4) = 3n + 11. What is n?
  24. 24.A father is 30 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?
  25. 25.Solve: 4p + 1 = 3p + 2. What is p?
  26. 26.Solve: x/3 + x/2 = 40. What is x?
  27. 27.Solve: m/2 + m/4 = 6. What is m?
  28. 28.Solve: 4(m − 2) = 2m + 4. What is m?
  29. 29.Solve: p/2 + p/6 = 4. What is p?
  30. 30.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?
  31. 31.Solve: 6x + 10 = 5x + 22. What is x?
  32. 32.Solve: 5(x − 3) = 3x + 5. What is x?
  33. 33.The length of a rectangle is 5 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  34. 34.The sum of four consecutive whole numbers is 82. What is the largest of them?
  35. 35.Solve: 5x + 1 = 2x + 4. What is x?
  36. 36.The sum of three consecutive whole numbers is 150. What is the smallest of them?
  37. 37.The length of a rectangle is 7 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 3 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  39. 39.Solve: 9x + 15 = 7x + 39. What is x?
  40. 40.Solve: 4n + 15 = 2n + 27. What is n?

Answer key

  1. 15
  2. 12
  3. 3
  4. 15
  5. 7
  6. 30
  7. 3
  8. 18
  9. 60
  10. 19
  11. 42
  12. 20
  13. 18
  14. 5
  15. 31
  16. 26
  17. 14
  18. 5
  19. 12
  20. 29
  21. 9
  22. 8
  23. 27
  24. 11
  25. 1
  26. 48
  27. 8
  28. 6
  29. 6
  30. 3
  31. 12
  32. 10
  33. 14
  34. 22
  35. 1
  36. 49
  37. 17
  38. 14
  39. 12
  40. 6

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