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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 112 · 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.A father is 18 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?
  2. 2.Solve: p/4 + p/3 = 35. What is p?
  3. 3.Solve: 5t + 11 = 4t + 19. What is t?
  4. 4.Solve: 6(n − 3) = 3n + 9. What is n?
  5. 5.Solve: x/6 + x/3 = 24. What is x?
  6. 6.The sum of two consecutive whole numbers is 119. What is the largest of them?
  7. 7.The sum of two consecutive whole numbers is 21. What is the smallest of them?
  8. 8.The length of a rectangle is 5 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  9. 9.The sum of two consecutive whole numbers is 11. What is the smallest of them?
  10. 10.Solve: y/2 + y/5 = 7. What is y?
  11. 11.A father is 8 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  12. 12.Solve: 5(n − 3) = 2n + 21. What is n?
  13. 13.Solve: 8n + 3 = 5n + 15. What is n?
  14. 14.Solve: 9n + 10 = n + 74. What is n?
  15. 15.Solve: 3(m − 2) = m + 20. What is m?
  16. 16.Solve: 7y + 1 = 5y + 11. What is y?
  17. 17.Solve: 4p + 17 = 2p + 27. What is p?
  18. 18.Solve: 8t + 4 = 5t + 16. What is t?
  19. 19.A father is 20 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?
  20. 20.Solve: 4(m − 5) = m + 7. What is m?
  21. 21.The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  22. 22.Solve: n/3 + n/2 = 15. What is n?
  23. 23.A father is 14 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  24. 24.Solve: 3t + 14 = t + 16. What is t?
  25. 25.Solve: 6p + 10 = 3p + 16. What is p?
  26. 26.The length of a rectangle is 9 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  27. 27.Solve: 3(p − 2) = 2p + 4. What is p?
  28. 28.A father is 33 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?
  29. 29.Solve: 6(p − 1) = 5p + 11. What is p?
  30. 30.Solve: 7y + 6 = 2y + 11. What is y?
  31. 31.Solve: 5(y − 3) = 2y + 33. What is y?
  32. 32.Solve: 6(x − 1) = 2x + 10. What is x?
  33. 33.The sum of four consecutive whole numbers is 134. What is the smallest of them?
  34. 34.Solve: m/5 + m/6 = 33. What is m?
  35. 35.Solve: 4(t − 2) = 2t + 26. What is t?
  36. 36.Solve: p/3 + p/2 = 30. What is p?
  37. 37.Solve: 3(y − 3) = 2y + 3. What is y?
  38. 38.Solve: m/4 + m/2 = 24. What is m?
  39. 39.The length of a rectangle is 5 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  40. 40.The length of a rectangle is 1 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?

Answer key

  1. 7
  2. 60
  3. 8
  4. 9
  5. 48
  6. 60
  7. 10
  8. 29
  9. 5
  10. 10
  11. 4
  12. 12
  13. 4
  14. 8
  15. 13
  16. 5
  17. 5
  18. 4
  19. 6
  20. 9
  21. 20
  22. 18
  23. 9
  24. 1
  25. 2
  26. 12
  27. 10
  28. 4
  29. 17
  30. 1
  31. 16
  32. 4
  33. 32
  34. 90
  35. 17
  36. 36
  37. 12
  38. 32
  39. 25
  40. 6

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