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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 57 · 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 13 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  2. 2.The sum of two consecutive whole numbers is 71. What is the smallest of them?
  3. 3.The sum of four consecutive whole numbers is 174. What is the smallest of them?
  4. 4.Solve: m/4 + m/3 = 56. What is m?
  5. 5.A father is 22 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?
  6. 6.Solve: m/4 + m/3 = 7. What is m?
  7. 7.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  8. 8.Solve: 3(m − 5) = 2m + 8. What is m?
  9. 9.A father is 22 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  10. 10.The sum of two consecutive whole numbers is 109. What is the smallest of them?
  11. 11.The length of a rectangle is 3 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  12. 12.Solve: 3(n − 4) = n + 2. What is n?
  13. 13.A father is 39 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?
  14. 14.The length of a rectangle is 9 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  15. 15.Solve: 3(x − 5) = 2x + 8. What is x?
  16. 16.The sum of three consecutive whole numbers is 105. What is the smallest of them?
  17. 17.Solve: 8t + 8 = 5t + 23. What is t?
  18. 18.Solve: t/5 + t/2 = 35. What is t?
  19. 19.The length of a rectangle is 4 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  20. 20.A father is 21 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  21. 21.The length of a rectangle is 11 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  22. 22.Solve: y/2 + y/5 = 42. What is y?
  23. 23.The length of a rectangle is 2 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  24. 24.Solve: n/4 + n/2 = 9. What is n?
  25. 25.The length of a rectangle is 1 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  26. 26.A father is 24 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?
  27. 27.Solve: n/2 + n/3 = 35. What is n?
  28. 28.The length of a rectangle is 12 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  29. 29.Solve: n/5 + n/6 = 44. What is n?
  30. 30.The sum of two consecutive whole numbers is 111. What is the largest of them?
  31. 31.Solve: 3(n − 5) = 2n + 5. What is n?
  32. 32.Solve: t/6 + t/5 = 11. What is t?
  33. 33.Solve: 3x + 3 = 2x + 4. What is x?
  34. 34.Solve: 3(p − 1) = p + 19. What is p?
  35. 35.Solve: 4(x − 2) = x + 4. What is x?
  36. 36.Solve: 7p + 9 = p + 39. What is p?
  37. 37.The sum of two consecutive whole numbers is 119. What is the largest of them?
  38. 38.Solve: 4y + 11 = y + 17. What is y?
  39. 39.Solve: 7t + 6 = 6t + 19. What is t?
  40. 40.Solve: t/2 + t/5 = 7. What is t?

Answer key

  1. 15
  2. 35
  3. 42
  4. 96
  5. 9
  6. 12
  7. 8
  8. 23
  9. 8
  10. 54
  11. 3
  12. 7
  13. 6
  14. 27
  15. 23
  16. 34
  17. 5
  18. 50
  19. 5
  20. 2
  21. 18
  22. 60
  23. 29
  24. 12
  25. 26
  26. 8
  27. 42
  28. 19
  29. 120
  30. 56
  31. 20
  32. 30
  33. 1
  34. 11
  35. 4
  36. 5
  37. 60
  38. 2
  39. 13
  40. 10

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