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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 857 · 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: 3(t − 2) = 2t + 5. What is t?
  2. 2.The length of a rectangle is 3 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  3. 3.Solve: x/4 + x/6 = 25. What is x?
  4. 4.The sum of three consecutive whole numbers is 78. What is the smallest of them?
  5. 5.Solve: 5(t − 1) = 2t + 25. What is t?
  6. 6.Solve: 4m + 1 = 2m + 31. What is m?
  7. 7.Solve: p/4 + p/3 = 14. What is p?
  8. 8.A father is 33 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  9. 9.A father is 26 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  10. 10.Solve: m/2 + m/6 = 32. What is m?
  11. 11.Solve: 3(p − 3) = p + 7. What is p?
  12. 12.The sum of two consecutive whole numbers is 27. What is the largest of them?
  13. 13.A father is 6 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  14. 14.Solve: 3(y − 4) = y + 2. What is y?
  15. 15.The length of a rectangle is 12 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  16. 16.Solve: 5(p − 1) = p + 23. What is p?
  17. 17.The length of a rectangle is 8 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
  18. 18.Solve: 6(n − 2) = 4n + 22. What is n?
  19. 19.The length of a rectangle is 4 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  20. 20.Solve: n/6 + n/2 = 20. What is n?
  21. 21.Solve: 6(x − 5) = 2x + 10. What is x?
  22. 22.The sum of two consecutive whole numbers is 77. What is the largest of them?
  23. 23.The sum of three consecutive whole numbers is 48. What is the smallest of them?
  24. 24.Solve: 6(y − 4) = 3y + 33. What is y?
  25. 25.The sum of four consecutive whole numbers is 98. What is the largest of them?
  26. 26.Solve: 8x + 11 = 3x + 26. What is x?
  27. 27.Solve: 6(t − 2) = t + 48. What is t?
  28. 28.Solve: n/2 + n/5 = 28. What is n?
  29. 29.Solve: 5(x − 2) = 2x + 2. What is x?
  30. 30.Solve: 5(t − 2) = t + 22. What is t?
  31. 31.Solve: p/3 + p/4 = 35. What is p?
  32. 32.Solve: 4m + 8 = 2m + 10. What is m?
  33. 33.The length of a rectangle is 1 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  34. 34.Solve: y/6 + y/3 = 3. What is y?
  35. 35.A father is 24 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  36. 36.A father is 32 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?
  37. 37.Solve: 3(m − 1) = m + 25. What is m?
  38. 38.Solve: 3y + 11 = 2y + 18. What is y?
  39. 39.The sum of two consecutive whole numbers is 35. What is the smallest of them?
  40. 40.The sum of four consecutive whole numbers is 158. What is the smallest of them?

Answer key

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

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