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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 630 · 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 10 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  2. 2.Solve: t/2 + t/6 = 24. What is t?
  3. 3.The sum of four consecutive whole numbers is 130. What is the smallest of them?
  4. 4.The sum of four consecutive whole numbers is 58. What is the smallest of them?
  5. 5.A father is 24 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  6. 6.A father is 26 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?
  7. 7.A father is 51 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  8. 8.The sum of two consecutive whole numbers is 45. What is the largest of them?
  9. 9.A father is 22 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?
  10. 10.The sum of two consecutive whole numbers is 121. What is the smallest of them?
  11. 11.The length of a rectangle is 15 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  12. 12.A father is 10 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  13. 13.The sum of two consecutive whole numbers is 111. What is the largest of them?
  14. 14.Solve: 4t + 5 = 2t + 31. What is t?
  15. 15.A father is 24 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?
  16. 16.Solve: n/3 + n/6 = 3. What is n?
  17. 17.Solve: 5(p − 1) = p + 19. What is p?
  18. 18.A father is 16 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: 5(y − 1) = 4y + 4. What is y?
  20. 20.A father is 8 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  21. 21.The length of a rectangle is 10 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  22. 22.Solve: 6p + 19 = 5p + 24. What is p?
  23. 23.Solve: y/2 + y/6 = 20. What is y?
  24. 24.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  25. 25.The sum of three consecutive whole numbers is 135. What is the largest of them?
  26. 26.The sum of four consecutive whole numbers is 166. What is the smallest of them?
  27. 27.The sum of four consecutive whole numbers is 42. What is the largest of them?
  28. 28.Solve: 8x + 12 = 5x + 30. What is x?
  29. 29.The sum of four consecutive whole numbers is 34. What is the smallest of them?
  30. 30.A father is 42 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?
  31. 31.The sum of two consecutive whole numbers is 73. What is the smallest of them?
  32. 32.The length of a rectangle is 8 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  33. 33.The sum of two consecutive whole numbers is 95. What is the largest of them?
  34. 34.The length of a rectangle is 13 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  35. 35.The sum of two consecutive whole numbers is 89. What is the smallest of them?
  36. 36.Solve: 5(m − 3) = 2m + 9. What is m?
  37. 37.Solve: x/5 + x/2 = 49. What is x?
  38. 38.Solve: 3(p − 4) = 2p + 3. What is p?
  39. 39.The sum of four consecutive whole numbers is 154. What is the smallest of them?
  40. 40.The sum of two consecutive whole numbers is 101. What is the largest of them?

Answer key

  1. 21
  2. 36
  3. 31
  4. 13
  5. 7
  6. 11
  7. 9
  8. 23
  9. 5
  10. 60
  11. 4
  12. 2
  13. 56
  14. 13
  15. 9
  16. 6
  17. 6
  18. 11
  19. 9
  20. 3
  21. 20
  22. 5
  23. 30
  24. 14
  25. 46
  26. 40
  27. 12
  28. 6
  29. 7
  30. 11
  31. 36
  32. 27
  33. 48
  34. 2
  35. 44
  36. 8
  37. 70
  38. 15
  39. 37
  40. 51

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