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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 789 · 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 5 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  2. 2.Solve: 4(n − 4) = n + 11. What is n?
  3. 3.The length of a rectangle is 11 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  4. 4.The sum of three consecutive whole numbers is 138. What is the smallest of them?
  5. 5.Solve: 4(m − 4) = 2m + 10. What is m?
  6. 6.Solve: 6(m − 1) = 4m + 14. What is m?
  7. 7.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  8. 8.Solve: 4m + 5 = m + 44. What is m?
  9. 9.The sum of four consecutive whole numbers is 62. What is the smallest of them?
  10. 10.The length of a rectangle is 13 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  11. 11.Solve: m/2 + m/4 = 3. What is m?
  12. 12.A father is 39 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  13. 13.Solve: 4(t − 2) = t + 4. What is t?
  14. 14.Solve: 6p + 5 = 2p + 45. What is p?
  15. 15.Solve: 6(n − 2) = 3n + 9. What is n?
  16. 16.Solve: 4(p − 4) = 3p + 12. What is p?
  17. 17.Solve: 5(p − 2) = 3p + 2. What is p?
  18. 18.Solve: y/4 + y/5 = 18. What is y?
  19. 19.Solve: n/3 + n/6 = 12. What is n?
  20. 20.Solve: y/6 + y/4 = 5. What is y?
  21. 21.The sum of two consecutive whole numbers is 69. What is the largest of them?
  22. 22.Solve: 6(n − 4) = 3n + 6. What is n?
  23. 23.A father is 39 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?
  24. 24.The length of a rectangle is 1 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  25. 25.The sum of three consecutive whole numbers is 42. What is the smallest of them?
  26. 26.Solve: 5p + 16 = p + 56. What is p?
  27. 27.Solve: 4(t − 4) = 3t + 9. What is t?
  28. 28.A father is 27 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  29. 29.Solve: 4n + 20 = n + 26. What is n?
  30. 30.The sum of two consecutive whole numbers is 103. What is the smallest of them?
  31. 31.The length of a rectangle is 5 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  32. 32.Solve: 7m + 16 = m + 82. What is m?
  33. 33.Solve: 3n + 16 = 2n + 23. What is n?
  34. 34.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  35. 35.The sum of two consecutive whole numbers is 35. What is the largest of them?
  36. 36.Solve: 7t + 13 = 5t + 17. What is t?
  37. 37.A father is 11 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: 5x + 20 = 2x + 62. What is x?
  39. 39.Solve: 3(p − 3) = p + 1. What is p?
  40. 40.The sum of three consecutive whole numbers is 126. What is the smallest of them?

Answer key

  1. 24
  2. 9
  3. 24
  4. 45
  5. 13
  6. 10
  7. 12
  8. 13
  9. 14
  10. 28
  11. 4
  12. 11
  13. 4
  14. 10
  15. 7
  16. 28
  17. 6
  18. 40
  19. 24
  20. 12
  21. 35
  22. 10
  23. 10
  24. 12
  25. 13
  26. 10
  27. 25
  28. 3
  29. 2
  30. 51
  31. 11
  32. 11
  33. 7
  34. 7
  35. 18
  36. 2
  37. 8
  38. 14
  39. 5
  40. 41

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