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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 973 · 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 12 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  2. 2.Solve: p/2 + p/3 = 5. What is p?
  3. 3.The length of a rectangle is 12 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  4. 4.Solve: n/4 + n/2 = 12. What is n?
  5. 5.Solve: 5p + 13 = 4p + 17. What is p?
  6. 6.Solve: 3y + 10 = y + 34. What is y?
  7. 7.Solve: n/3 + n/5 = 56. What is n?
  8. 8.Solve: 3(p − 3) = 2p + 10. What is p?
  9. 9.Solve: 4(p − 3) = 3p + 9. What is p?
  10. 10.Solve: m/3 + m/4 = 21. What is m?
  11. 11.Solve: 3(n − 1) = 2n + 13. What is n?
  12. 12.A father is 26 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?
  13. 13.Solve: m/3 + m/6 = 3. What is m?
  14. 14.Solve: 5x + 19 = x + 63. What is x?
  15. 15.The sum of three consecutive whole numbers is 126. What is the largest of them?
  16. 16.Solve: 8t + 7 = 2t + 43. What is t?
  17. 17.Solve: 6(y − 4) = 3y + 24. What is y?
  18. 18.The sum of three consecutive whole numbers is 45. What is the largest of them?
  19. 19.The length of a rectangle is 4 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  20. 20.A father is 13 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  21. 21.Solve: 9p + 7 = 8p + 11. What is p?
  22. 22.Solve: 6(p − 1) = p + 9. What is p?
  23. 23.Solve: 3(m − 5) = 2m + 5. What is m?
  24. 24.Solve: y/2 + y/6 = 24. What is y?
  25. 25.The sum of two consecutive whole numbers is 97. What is the smallest of them?
  26. 26.A father is 33 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?
  27. 27.The sum of three consecutive whole numbers is 171. What is the smallest of them?
  28. 28.A father is 12 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  29. 29.Solve: 3p + 12 = p + 36. What is p?
  30. 30.The length of a rectangle is 3 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  31. 31.The sum of three consecutive whole numbers is 96. What is the smallest of them?
  32. 32.The length of a rectangle is 4 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  33. 33.Solve: 4(m − 4) = m + 14. What is m?
  34. 34.Solve: 9x + 4 = 8x + 9. What is x?
  35. 35.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  36. 36.The sum of four consecutive whole numbers is 234. What is the smallest of them?
  37. 37.Solve: 5x + 3 = 2x + 12. What is x?
  38. 38.Solve: y/3 + y/5 = 8. What is y?
  39. 39.A father is 54 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?
  40. 40.Solve: t/5 + t/2 = 56. What is t?

Answer key

  1. 16
  2. 6
  3. 4
  4. 16
  5. 4
  6. 12
  7. 105
  8. 19
  9. 21
  10. 36
  11. 16
  12. 7
  13. 6
  14. 11
  15. 43
  16. 6
  17. 16
  18. 16
  19. 7
  20. 9
  21. 4
  22. 3
  23. 20
  24. 36
  25. 48
  26. 8
  27. 56
  28. 6
  29. 12
  30. 8
  31. 31
  32. 10
  33. 10
  34. 5
  35. 8
  36. 57
  37. 3
  38. 15
  39. 11
  40. 80

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