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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 197 · 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: x/6 + x/2 = 12. What is x?
  2. 2.Solve: 9n + 13 = 4n + 18. What is n?
  3. 3.A father is 17 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  4. 4.A father is 24 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  5. 5.Solve: p/5 + p/6 = 77. What is p?
  6. 6.Solve: n/2 + n/4 = 21. What is n?
  7. 7.The sum of two consecutive whole numbers is 81. What is the smallest of them?
  8. 8.Solve: 4(p − 5) = 3p + 7. What is p?
  9. 9.Solve: 8x + 1 = 7x + 14. What is x?
  10. 10.The sum of two consecutive whole numbers is 33. What is the smallest of them?
  11. 11.The length of a rectangle is 12 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  12. 12.Solve: 3(p − 3) = p + 5. What is p?
  13. 13.The length of a rectangle is 3 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  14. 14.Solve: 3(t − 1) = t + 9. What is t?
  15. 15.The length of a rectangle is 14 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  16. 16.A father is 30 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?
  17. 17.Solve: 3x + 17 = x + 23. What is x?
  18. 18.Solve: 3y + 19 = 2y + 33. What is y?
  19. 19.A father is 20 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?
  20. 20.Solve: 8p + 4 = 4p + 28. What is p?
  21. 21.Solve: p/2 + p/6 = 28. What is p?
  22. 22.The sum of three consecutive whole numbers is 72. What is the smallest of them?
  23. 23.Solve: 3(y − 5) = y + 13. What is y?
  24. 24.The sum of three consecutive whole numbers is 168. What is the largest of them?
  25. 25.Solve: m/2 + m/6 = 28. What is m?
  26. 26.Solve: 3x + 12 = 2x + 25. What is x?
  27. 27.Solve: y/6 + y/2 = 28. What is y?
  28. 28.Solve: 3(m − 5) = m + 19. What is m?
  29. 29.A father is 16 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  30. 30.Solve: n/3 + n/5 = 8. What is n?
  31. 31.The length of a rectangle is 2 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  32. 32.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  33. 33.The sum of four consecutive whole numbers is 58. What is the largest of them?
  34. 34.The sum of two consecutive whole numbers is 111. What is the largest of them?
  35. 35.Solve: 6(n − 3) = n + 62. What is n?
  36. 36.The length of a rectangle is 6 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  37. 37.The length of a rectangle is 3 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  38. 38.The sum of three consecutive whole numbers is 63. What is the smallest of them?
  39. 39.Solve: 5(y − 5) = y + 47. What is y?
  40. 40.The sum of four consecutive whole numbers is 202. What is the smallest of them?

Answer key

  1. 18
  2. 1
  3. 11
  4. 5
  5. 210
  6. 28
  7. 40
  8. 27
  9. 13
  10. 16
  11. 22
  12. 7
  13. 29
  14. 6
  15. 22
  16. 9
  17. 3
  18. 14
  19. 8
  20. 6
  21. 42
  22. 23
  23. 14
  24. 57
  25. 42
  26. 13
  27. 42
  28. 17
  29. 3
  30. 15
  31. 4
  32. 28
  33. 16
  34. 56
  35. 16
  36. 26
  37. 18
  38. 20
  39. 18
  40. 49

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