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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 339 · 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: n/5 + n/4 = 36. What is n?
  2. 2.The sum of two consecutive whole numbers is 105. What is the smallest of them?
  3. 3.Solve: 3(x − 4) = 2x + 10. What is x?
  4. 4.A father is 11 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  5. 5.Solve: 6(x − 2) = 4x + 18. What is x?
  6. 6.Solve: t/2 + t/5 = 42. What is t?
  7. 7.The length of a rectangle is 10 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  8. 8.Solve: 5(x − 5) = x + 23. What is x?
  9. 9.Solve: 5p + 15 = 3p + 29. What is p?
  10. 10.The length of a rectangle is 1 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  11. 11.Solve: m/5 + m/2 = 35. What is m?
  12. 12.A father is 28 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?
  13. 13.Solve: 4(y − 1) = 3y + 10. What is y?
  14. 14.Solve: 4(m − 1) = m + 23. What is m?
  15. 15.Solve: 6(t − 1) = 3t + 27. What is t?
  16. 16.The sum of four consecutive whole numbers is 162. What is the largest of them?
  17. 17.A father is 42 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  18. 18.The sum of two consecutive whole numbers is 27. What is the smallest of them?
  19. 19.Solve: 7y + 7 = 2y + 47. What is y?
  20. 20.Solve: 5y + 3 = 2y + 12. What is y?
  21. 21.The sum of three consecutive whole numbers is 39. What is the largest of them?
  22. 22.Solve: 5(m − 4) = m + 4. What is m?
  23. 23.Solve: 3(p − 3) = p + 21. What is p?
  24. 24.Solve: n/6 + n/3 = 3. What is n?
  25. 25.Solve: 3(p − 1) = p + 25. What is p?
  26. 26.Solve: 5(y − 5) = 4y + 12. What is y?
  27. 27.Solve: 6(n − 1) = 4n + 14. What is n?
  28. 28.The sum of two consecutive whole numbers is 117. What is the largest of them?
  29. 29.Solve: m/2 + m/4 = 6. What is m?
  30. 30.Solve: x/3 + x/5 = 48. What is x?
  31. 31.Solve: t/4 + t/5 = 72. What is t?
  32. 32.The sum of two consecutive whole numbers is 67. What is the largest of them?
  33. 33.A father is 12 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?
  34. 34.The sum of three consecutive whole numbers is 84. What is the smallest of them?
  35. 35.A father is 4 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  36. 36.A father is 6 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  37. 37.Solve: y/6 + y/2 = 16. What is y?
  38. 38.The sum of two consecutive whole numbers is 53. What is the largest of them?
  39. 39.Solve: 3(n − 3) = n + 1. What is n?
  40. 40.Solve: 5p + 2 = 4p + 17. What is p?

Answer key

  1. 80
  2. 52
  3. 22
  4. 10
  5. 15
  6. 60
  7. 18
  8. 12
  9. 7
  10. 10
  11. 50
  12. 12
  13. 14
  14. 9
  15. 11
  16. 42
  17. 8
  18. 13
  19. 8
  20. 3
  21. 14
  22. 6
  23. 15
  24. 6
  25. 14
  26. 37
  27. 10
  28. 59
  29. 8
  30. 90
  31. 160
  32. 34
  33. 4
  34. 27
  35. 3
  36. 2
  37. 24
  38. 27
  39. 5
  40. 15

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