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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 431 · 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: 5(p − 1) = p + 7. What is p?
  2. 2.Solve: 6(t − 1) = 2t + 6. What is t?
  3. 3.Solve: 7t + 16 = t + 34. What is t?
  4. 4.Solve: x/4 + x/3 = 42. What is x?
  5. 5.Solve: 6(x − 3) = 3x + 39. What is x?
  6. 6.The length of a rectangle is 12 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  7. 7.Solve: m/2 + m/4 = 6. What is m?
  8. 8.A father is 30 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?
  9. 9.Solve: 5(y − 4) = y + 28. What is y?
  10. 10.The sum of four consecutive whole numbers is 246. What is the smallest of them?
  11. 11.The sum of three consecutive whole numbers is 96. What is the largest of them?
  12. 12.A father is 39 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?
  13. 13.Solve: 6x + 18 = 5x + 32. What is x?
  14. 14.Solve: p/4 + p/2 = 12. What is p?
  15. 15.The sum of four consecutive whole numbers is 42. What is the smallest of them?
  16. 16.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  17. 17.Solve: n/3 + n/2 = 35. What is n?
  18. 18.Solve: 6(y − 4) = 2y + 28. What is y?
  19. 19.The sum of four consecutive whole numbers is 82. What is the largest of them?
  20. 20.Solve: n/6 + n/2 = 20. What is n?
  21. 21.The length of a rectangle is 1 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  22. 22.A father is 5 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  23. 23.The sum of four consecutive whole numbers is 166. What is the smallest of them?
  24. 24.A father is 13 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  25. 25.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?
  26. 26.Solve: m/2 + m/5 = 35. What is m?
  27. 27.Solve: 5x + 10 = 3x + 26. What is x?
  28. 28.Solve: 4(x − 3) = x + 33. What is x?
  29. 29.Solve: 3(x − 4) = x + 8. What is x?
  30. 30.Solve: 4(t − 5) = 2t + 24. What is t?
  31. 31.Solve: 3(m − 5) = 2m + 9. What is m?
  32. 32.The length of a rectangle is 6 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  33. 33.Solve: 6(y − 4) = 2y + 12. What is y?
  34. 34.A father is 33 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?
  35. 35.The length of a rectangle is 1 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  36. 36.Solve: 5t + 13 = 2t + 43. What is t?
  37. 37.A father is 8 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  38. 38.Solve: x/5 + x/6 = 44. What is x?
  39. 39.Solve: 4m + 9 = 3m + 21. What is m?
  40. 40.The sum of four consecutive whole numbers is 150. What is the largest of them?

Answer key

  1. 3
  2. 3
  3. 3
  4. 72
  5. 19
  6. 23
  7. 8
  8. 9
  9. 12
  10. 60
  11. 33
  12. 6
  13. 14
  14. 16
  15. 9
  16. 9
  17. 42
  18. 13
  19. 22
  20. 30
  21. 15
  22. 2
  23. 40
  24. 10
  25. 9
  26. 50
  27. 8
  28. 15
  29. 10
  30. 22
  31. 24
  32. 17
  33. 9
  34. 5
  35. 9
  36. 10
  37. 3
  38. 120
  39. 12
  40. 39

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