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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 157 · 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 sum of two consecutive whole numbers is 55. What is the smallest of them?
  2. 2.A father is 14 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  3. 3.Solve: 4(p − 1) = 2p + 10. What is p?
  4. 4.Solve: t/3 + t/5 = 8. What is t?
  5. 5.Solve: 5n + 19 = 4n + 21. What is n?
  6. 6.The length of a rectangle is 12 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  7. 7.The length of a rectangle is 7 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  8. 8.Solve: 5(x − 4) = 3x + 20. What is x?
  9. 9.The length of a rectangle is 4 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  10. 10.Solve: m/4 + m/5 = 54. What is m?
  11. 11.The sum of three consecutive whole numbers is 18. What is the largest of them?
  12. 12.Solve: 4(n − 1) = n + 35. What is n?
  13. 13.Solve: 5(p − 1) = 3p + 15. What is p?
  14. 14.Solve: 7p + 12 = 3p + 20. What is p?
  15. 15.Solve: p/4 + p/2 = 9. What is p?
  16. 16.The length of a rectangle is 11 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  17. 17.Solve: 6x + 8 = 2x + 28. What is x?
  18. 18.Solve: 9p + 8 = 3p + 32. What is p?
  19. 19.The length of a rectangle is 13 cm more than its width. Its perimeter is 146 cm. What is its width (in cm)?
  20. 20.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  21. 21.Solve: 4(y − 5) = 2y + 14. What is y?
  22. 22.Solve: 7m + 17 = 6m + 28. What is m?
  23. 23.Solve: n/3 + n/2 = 5. What is n?
  24. 24.The length of a rectangle is 8 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  25. 25.Solve: 4(p − 4) = 2p + 10. What is p?
  26. 26.The sum of four consecutive whole numbers is 90. What is the smallest of them?
  27. 27.Solve: 3(n − 1) = 2n + 3. What is n?
  28. 28.Solve: 9p + 6 = 3p + 78. What is p?
  29. 29.Solve: 6x + 19 = x + 29. What is x?
  30. 30.Solve: 6(t − 4) = 2t + 28. What is t?
  31. 31.Solve: 4(x − 2) = x + 16. What is x?
  32. 32.Solve: 5(p − 2) = p + 10. What is p?
  33. 33.Solve: 6(n − 4) = 5n + 6. What is n?
  34. 34.Solve: 3p + 2 = p + 10. What is p?
  35. 35.Solve: 5(t − 4) = 4t + 2. What is t?
  36. 36.A father is 10 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?
  37. 37.A father is 39 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?
  38. 38.Solve: 7t + 2 = 4t + 20. What is t?
  39. 39.The length of a rectangle is 15 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  40. 40.Solve: 4(p − 2) = 3p + 10. What is p?

Answer key

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

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