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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 691 · 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: 3(y − 4) = y + 8. What is y?
  2. 2.Solve: t/5 + t/2 = 56. What is t?
  3. 3.The sum of three consecutive whole numbers is 102. What is the largest of them?
  4. 4.Solve: 4(x − 4) = 3x + 13. What is x?
  5. 5.The sum of three consecutive whole numbers is 174. What is the largest of them?
  6. 6.The length of a rectangle is 14 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  7. 7.Solve: 6x + 5 = 4x + 33. What is x?
  8. 8.Solve: 3x + 2 = 2x + 5. What is x?
  9. 9.The length of a rectangle is 11 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  10. 10.The length of a rectangle is 14 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  11. 11.Solve: 8t + 9 = 5t + 15. What is t?
  12. 12.The length of a rectangle is 6 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  13. 13.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?
  14. 14.Solve: 4m + 12 = m + 39. What is m?
  15. 15.Solve: 5(m − 4) = m + 16. What is m?
  16. 16.A father is 24 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.The sum of three consecutive whole numbers is 81. What is the smallest of them?
  18. 18.Solve: 8t + 15 = t + 71. What is t?
  19. 19.Solve: 3x + 3 = 2x + 4. What is x?
  20. 20.The length of a rectangle is 12 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  21. 21.The sum of three consecutive whole numbers is 84. What is the largest of them?
  22. 22.Solve: n/6 + n/2 = 32. What is n?
  23. 23.Solve: t/3 + t/4 = 35. What is t?
  24. 24.Solve: x/3 + x/6 = 12. What is x?
  25. 25.Solve: 4(t − 4) = t + 23. What is t?
  26. 26.The sum of two consecutive whole numbers is 21. What is the smallest of them?
  27. 27.Solve: 6(y − 3) = 4y + 2. What is y?
  28. 28.The sum of three consecutive whole numbers is 159. What is the largest of them?
  29. 29.Solve: 4(t − 1) = t + 17. What is t?
  30. 30.The length of a rectangle is 15 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  31. 31.The length of a rectangle is 14 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  32. 32.Solve: 3y + 9 = 2y + 16. What is y?
  33. 33.Solve: 9x + 8 = 2x + 106. What is x?
  34. 34.A father is 26 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?
  35. 35.A father is 42 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  36. 36.Solve: 9t + 14 = 4t + 24. What is t?
  37. 37.Solve: 3(n − 4) = n + 2. What is n?
  38. 38.The sum of four consecutive whole numbers is 170. What is the smallest of them?
  39. 39.The sum of four consecutive whole numbers is 142. What is the largest of them?
  40. 40.Solve: 7n + 1 = 5n + 15. What is n?

Answer key

  1. 10
  2. 80
  3. 35
  4. 29
  5. 59
  6. 24
  7. 14
  8. 3
  9. 19
  10. 16
  11. 2
  12. 14
  13. 3
  14. 9
  15. 9
  16. 6
  17. 26
  18. 8
  19. 1
  20. 16
  21. 29
  22. 48
  23. 60
  24. 24
  25. 13
  26. 10
  27. 10
  28. 54
  29. 7
  30. 4
  31. 20
  32. 7
  33. 14
  34. 7
  35. 10
  36. 2
  37. 7
  38. 41
  39. 37
  40. 7

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