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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 266 · 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.Solve: 4m + 18 = m + 24. What is m?
  2. 2.Solve: 9m + 13 = 4m + 43. What is m?
  3. 3.Solve: 4(m − 1) = 2m + 18. What is m?
  4. 4.The length of a rectangle is 13 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  5. 5.Solve: 3(t − 4) = t + 14. What is t?
  6. 6.The length of a rectangle is 2 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  7. 7.Solve: 6m + 7 = 3m + 25. What is m?
  8. 8.Solve: 3(n − 4) = n + 18. What is n?
  9. 9.Solve: 5(n − 4) = 4n + 9. What is n?
  10. 10.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?
  11. 11.A father is 7 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  12. 12.The sum of two consecutive whole numbers is 81. What is the smallest of them?
  13. 13.The sum of three consecutive whole numbers is 117. What is the smallest of them?
  14. 14.Solve: 8p + 14 = 5p + 59. What is p?
  15. 15.Solve: 4(m − 5) = m + 4. What is m?
  16. 16.Solve: 3n + 4 = n + 30. What is n?
  17. 17.Solve: 3(p − 1) = 2p + 13. What is p?
  18. 18.Solve: p/2 + p/6 = 16. What is p?
  19. 19.A father is 13 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  20. 20.A father is 39 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?
  21. 21.The length of a rectangle is 15 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  22. 22.Solve: 4(y − 1) = y + 35. What is y?
  23. 23.Solve: x/3 + x/2 = 10. What is x?
  24. 24.The sum of four consecutive whole numbers is 162. What is the largest of them?
  25. 25.Solve: p/6 + p/3 = 24. What is p?
  26. 26.Solve: 4x + 17 = x + 44. What is x?
  27. 27.Solve: x/3 + x/6 = 6. What is x?
  28. 28.Solve: n/6 + n/3 = 15. What is n?
  29. 29.Solve: 5(y − 3) = 2y + 15. What is y?
  30. 30.A father is 12 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?
  31. 31.A father is 16 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  32. 32.Solve: 6(x − 2) = 2x + 28. What is x?
  33. 33.A father is 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  34. 34.The length of a rectangle is 1 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  35. 35.Solve: t/2 + t/3 = 15. What is t?
  36. 36.The length of a rectangle is 4 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  37. 37.The sum of two consecutive whole numbers is 119. What is the largest of them?
  38. 38.The length of a rectangle is 4 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  39. 39.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  40. 40.Solve: 8p + 18 = 3p + 23. What is p?

Answer key

  1. 2
  2. 6
  3. 11
  4. 6
  5. 13
  6. 21
  7. 6
  8. 15
  9. 29
  10. 10
  11. 6
  12. 40
  13. 38
  14. 15
  15. 8
  16. 13
  17. 16
  18. 24
  19. 8
  20. 5
  21. 15
  22. 13
  23. 12
  24. 42
  25. 48
  26. 9
  27. 12
  28. 30
  29. 10
  30. 2
  31. 9
  32. 10
  33. 5
  34. 19
  35. 18
  36. 18
  37. 60
  38. 26
  39. 28
  40. 1

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