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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 897 · 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 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?
  2. 2.Solve: y/4 + y/5 = 9. What is y?
  3. 3.The length of a rectangle is 8 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  4. 4.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  5. 5.Solve: 3(t − 1) = t + 25. What is t?
  6. 6.Solve: p/6 + p/2 = 8. What is p?
  7. 7.Solve: 9t + 10 = t + 66. What is t?
  8. 8.Solve: 4(p − 1) = p + 8. What is p?
  9. 9.Solve: 3(t − 1) = t + 9. What is t?
  10. 10.Solve: 5(t − 5) = 3t + 13. What is t?
  11. 11.The length of a rectangle is 6 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
  12. 12.Solve: 5(x − 3) = 3x + 1. What is x?
  13. 13.Solve: 4(t − 5) = t + 10. What is t?
  14. 14.Solve: 6(p − 1) = 4p + 6. What is p?
  15. 15.Solve: x/4 + x/2 = 18. What is x?
  16. 16.The length of a rectangle is 4 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
  17. 17.Solve: 3(x − 3) = 2x + 11. What is x?
  18. 18.Solve: 8x + 10 = 4x + 66. What is x?
  19. 19.Solve: y/2 + y/4 = 12. What is y?
  20. 20.Solve: m/2 + m/3 = 5. What is m?
  21. 21.Solve: m/4 + m/2 = 15. What is m?
  22. 22.The length of a rectangle is 5 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  23. 23.The sum of four consecutive whole numbers is 122. What is the smallest of them?
  24. 24.The length of a rectangle is 12 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  25. 25.The sum of two consecutive whole numbers is 43. What is the smallest of them?
  26. 26.Solve: 4(p − 1) = p + 5. What is p?
  27. 27.Solve: p/6 + p/2 = 28. What is p?
  28. 28.Solve: x/4 + x/2 = 9. What is x?
  29. 29.Solve: 6(y − 4) = 2y + 8. What is y?
  30. 30.Solve: x/5 + x/2 = 21. What is x?
  31. 31.Solve: 6p + 11 = p + 16. What is p?
  32. 32.The sum of two consecutive whole numbers is 103. What is the smallest of them?
  33. 33.Solve: 5(n − 1) = 3n + 7. What is n?
  34. 34.Solve: 4(p − 4) = 2p + 2. What is p?
  35. 35.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?
  36. 36.A father is 3 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  37. 37.A father is 57 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?
  38. 38.Solve: 6(y − 3) = 4y + 2. What is y?
  39. 39.Solve: 3(y − 5) = y + 15. What is y?
  40. 40.The sum of three consecutive whole numbers is 174. What is the largest of them?

Answer key

  1. 6
  2. 20
  3. 3
  4. 2
  5. 14
  6. 12
  7. 7
  8. 4
  9. 6
  10. 19
  11. 30
  12. 8
  13. 10
  14. 6
  15. 24
  16. 2
  17. 20
  18. 14
  19. 16
  20. 6
  21. 20
  22. 24
  23. 29
  24. 7
  25. 21
  26. 3
  27. 42
  28. 12
  29. 8
  30. 30
  31. 1
  32. 51
  33. 6
  34. 9
  35. 9
  36. 2
  37. 11
  38. 10
  39. 15
  40. 59

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