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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 442 · 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 15 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  2. 2.Solve: 5m + 6 = 4m + 7. What is m?
  3. 3.Solve: 8t + 8 = 4t + 12. What is t?
  4. 4.Solve: 5n + 20 = n + 24. What is n?
  5. 5.Solve: t/3 + t/2 = 40. What is t?
  6. 6.Solve: 4(m − 3) = m + 12. What is m?
  7. 7.The sum of three consecutive whole numbers is 144. What is the smallest of them?
  8. 8.The sum of four consecutive whole numbers is 78. What is the smallest of them?
  9. 9.Solve: t/6 + t/2 = 4. What is t?
  10. 10.The sum of two consecutive whole numbers is 45. What is the smallest of them?
  11. 11.The length of a rectangle is 8 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  12. 12.The length of a rectangle is 8 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  13. 13.The length of a rectangle is 10 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  14. 14.A father is 40 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  15. 15.The length of a rectangle is 15 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  16. 16.The length of a rectangle is 14 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  17. 17.Solve: 7y + 14 = 2y + 64. What is y?
  18. 18.Solve: 6p + 8 = p + 53. What is p?
  19. 19.Solve: m/4 + m/6 = 35. What is m?
  20. 20.The sum of two consecutive whole numbers is 25. What is the largest of them?
  21. 21.Solve: m/5 + m/6 = 22. What is m?
  22. 22.The sum of two consecutive whole numbers is 31. What is the smallest of them?
  23. 23.Solve: 4t + 4 = 2t + 6. What is t?
  24. 24.The sum of two consecutive whole numbers is 71. What is the smallest of them?
  25. 25.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?
  26. 26.Solve: x/5 + x/3 = 40. What is x?
  27. 27.The sum of four consecutive whole numbers is 94. What is the smallest of them?
  28. 28.A father is 27 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?
  29. 29.Solve: 5(m − 1) = 3m + 21. What is m?
  30. 30.Solve: 5m + 16 = 4m + 23. What is m?
  31. 31.A father is 18 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  32. 32.Solve: t/4 + t/3 = 21. What is t?
  33. 33.Solve: m/2 + m/3 = 25. What is m?
  34. 34.The length of a rectangle is 2 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  35. 35.Solve: n/5 + n/2 = 49. What is n?
  36. 36.The length of a rectangle is 2 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  37. 37.Solve: n/3 + n/2 = 40. What is n?
  38. 38.Solve: n/2 + n/3 = 20. What is n?
  39. 39.The length of a rectangle is 12 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  40. 40.A father is 8 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?

Answer key

  1. 11
  2. 1
  3. 1
  4. 1
  5. 48
  6. 8
  7. 47
  8. 18
  9. 6
  10. 22
  11. 10
  12. 18
  13. 23
  14. 12
  15. 7
  16. 17
  17. 10
  18. 9
  19. 84
  20. 13
  21. 60
  22. 15
  23. 1
  24. 35
  25. 6
  26. 75
  27. 22
  28. 6
  29. 13
  30. 7
  31. 10
  32. 36
  33. 30
  34. 14
  35. 70
  36. 30
  37. 48
  38. 24
  39. 18
  40. 3

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