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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 851 · 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: 4(x − 1) = x + 26. What is x?
  2. 2.Solve: 7n + 13 = 2n + 68. What is n?
  3. 3.A father is 11 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  4. 4.The length of a rectangle is 10 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  5. 5.Solve: t/4 + t/2 = 3. What is t?
  6. 6.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  7. 7.Solve: 6(n − 5) = n + 40. What is n?
  8. 8.Solve: n/3 + n/5 = 16. What is n?
  9. 9.Solve: p/3 + p/2 = 5. What is p?
  10. 10.The sum of four consecutive whole numbers is 230. What is the smallest of them?
  11. 11.Solve: 7m + 19 = 3m + 35. What is m?
  12. 12.Solve: 3p + 1 = 2p + 13. What is p?
  13. 13.Solve: 8p + 2 = 2p + 8. What is p?
  14. 14.Solve: y/4 + y/3 = 56. What is y?
  15. 15.A father is 30 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?
  16. 16.Solve: t/2 + t/6 = 28. What is t?
  17. 17.Solve: 6(x − 1) = 2x + 6. What is x?
  18. 18.Solve: p/3 + p/4 = 42. What is p?
  19. 19.A father is 54 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?
  20. 20.Solve: 4x + 12 = 2x + 28. What is x?
  21. 21.Solve: 3(p − 4) = p + 2. What is p?
  22. 22.Solve: t/2 + t/6 = 16. What is t?
  23. 23.A father is 13 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  24. 24.A father is 10 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  25. 25.Solve: x/6 + x/3 = 18. What is x?
  26. 26.Solve: 4(p − 1) = 3p + 11. What is p?
  27. 27.The length of a rectangle is 3 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  28. 28.Solve: 8t + 10 = 4t + 22. What is t?
  29. 29.The sum of two consecutive whole numbers is 105. What is the smallest of them?
  30. 30.The sum of three consecutive whole numbers is 126. What is the largest of them?
  31. 31.The sum of four consecutive whole numbers is 78. What is the smallest of them?
  32. 32.Solve: 4(x − 3) = 3x + 2. What is x?
  33. 33.The length of a rectangle is 3 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  34. 34.Solve: 3(p − 5) = p + 25. What is p?
  35. 35.Solve: 3t + 3 = 2t + 4. What is t?
  36. 36.The length of a rectangle is 6 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  37. 37.Solve: 6(y − 5) = y + 20. What is y?
  38. 38.The length of a rectangle is 13 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  39. 39.Solve: 7n + 15 = 4n + 51. What is n?
  40. 40.Solve: x/3 + x/2 = 15. What is x?

Answer key

  1. 10
  2. 11
  3. 9
  4. 15
  5. 4
  6. 28
  7. 14
  8. 30
  9. 6
  10. 56
  11. 4
  12. 12
  13. 1
  14. 96
  15. 12
  16. 42
  17. 3
  18. 72
  19. 10
  20. 8
  21. 7
  22. 24
  23. 6
  24. 6
  25. 36
  26. 15
  27. 3
  28. 3
  29. 52
  30. 43
  31. 18
  32. 14
  33. 24
  34. 20
  35. 1
  36. 24
  37. 10
  38. 11
  39. 12
  40. 18

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