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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 191 · 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 9 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  2. 2.Solve: 7x + 14 = x + 104. What is x?
  3. 3.Solve: y/5 + y/4 = 18. What is y?
  4. 4.Solve: y/5 + y/4 = 9. What is y?
  5. 5.Solve: 3(t − 5) = 2t + 2. What is t?
  6. 6.The sum of two consecutive whole numbers is 55. What is the smallest of them?
  7. 7.A father is 20 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  8. 8.A father is 42 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?
  9. 9.Solve: 6(x − 1) = 2x + 6. What is x?
  10. 10.A father is 28 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?
  11. 11.Solve: 6(n − 1) = 4n + 8. What is n?
  12. 12.The sum of two consecutive whole numbers is 13. What is the smallest of them?
  13. 13.Solve: 4p + 14 = p + 32. What is p?
  14. 14.Solve: 4(y − 1) = 3y + 13. What is y?
  15. 15.The sum of four consecutive whole numbers is 38. What is the largest of them?
  16. 16.Solve: 6p + 13 = 2p + 65. What is p?
  17. 17.Solve: 3(t − 4) = 2t + 3. What is t?
  18. 18.Solve: m/2 + m/6 = 28. What is m?
  19. 19.Solve: m/6 + m/5 = 33. What is m?
  20. 20.Solve: m/4 + m/6 = 40. What is m?
  21. 21.The sum of four consecutive whole numbers is 58. What is the largest of them?
  22. 22.The length of a rectangle is 7 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  23. 23.Solve: m/3 + m/2 = 35. What is m?
  24. 24.A father is 10 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  25. 25.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?
  26. 26.The length of a rectangle is 10 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  27. 27.The length of a rectangle is 12 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  28. 28.Solve: 4n + 1 = n + 25. What is n?
  29. 29.Solve: 7x + 13 = 6x + 18. What is x?
  30. 30.Solve: p/2 + p/3 = 5. What is p?
  31. 31.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  32. 32.Solve: 9x + 6 = 3x + 60. What is x?
  33. 33.Solve: 6(p − 2) = p + 43. What is p?
  34. 34.Solve: 3y + 13 = 2y + 15. What is y?
  35. 35.The sum of three consecutive whole numbers is 39. What is the largest of them?
  36. 36.The length of a rectangle is 1 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  37. 37.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: 3(m − 3) = m + 5. What is m?
  39. 39.Solve: 6(x − 2) = 5x + 3. What is x?
  40. 40.Solve: x/4 + x/2 = 12. What is x?

Answer key

  1. 6
  2. 15
  3. 40
  4. 20
  5. 17
  6. 27
  7. 9
  8. 7
  9. 3
  10. 10
  11. 7
  12. 6
  13. 6
  14. 17
  15. 11
  16. 13
  17. 15
  18. 42
  19. 90
  20. 96
  21. 16
  22. 18
  23. 42
  24. 5
  25. 4
  26. 25
  27. 6
  28. 8
  29. 5
  30. 6
  31. 28
  32. 9
  33. 11
  34. 2
  35. 14
  36. 13
  37. 4
  38. 7
  39. 15
  40. 16

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