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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 13 · 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: t/2 + t/6 = 12. What is t?
  2. 2.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  3. 3.A father is 10 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  4. 4.The length of a rectangle is 15 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  5. 5.Solve: x/3 + x/2 = 30. What is x?
  6. 6.Solve: 3(p − 4) = p + 12. What is p?
  7. 7.A father is 20 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?
  8. 8.Solve: 3y + 4 = y + 18. What is y?
  9. 9.Solve: m/3 + m/2 = 25. What is m?
  10. 10.Solve: n/3 + n/6 = 6. What is n?
  11. 11.Solve: p/3 + p/4 = 14. What is p?
  12. 12.Solve: 3(x − 3) = x + 1. What is x?
  13. 13.The sum of three consecutive whole numbers is 84. What is the smallest of them?
  14. 14.Solve: 3(n − 2) = 2n + 3. What is n?
  15. 15.The length of a rectangle is 3 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  16. 16.Solve: n/3 + n/6 = 24. What is n?
  17. 17.The sum of three consecutive whole numbers is 99. What is the smallest of them?
  18. 18.The length of a rectangle is 1 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  19. 19.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  20. 20.The sum of four consecutive whole numbers is 106. What is the smallest of them?
  21. 21.Solve: n/4 + n/2 = 15. What is n?
  22. 22.The sum of four consecutive whole numbers is 98. What is the smallest of them?
  23. 23.Solve: x/2 + x/4 = 21. What is x?
  24. 24.Solve: p/5 + p/4 = 36. What is p?
  25. 25.Solve: 9x + 15 = 3x + 81. What is x?
  26. 26.Solve: 3y + 13 = y + 31. What is y?
  27. 27.Solve: y/2 + y/4 = 6. What is y?
  28. 28.A father is 12 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  29. 29.A father is 51 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?
  30. 30.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  31. 31.A father is 16 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  32. 32.Solve: 4(n − 4) = n + 8. What is n?
  33. 33.Solve: 5p + 13 = p + 17. What is p?
  34. 34.A father is 34 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  35. 35.Solve: 5x + 3 = x + 11. What is x?
  36. 36.Solve: 4p + 6 = 2p + 8. What is p?
  37. 37.The sum of two consecutive whole numbers is 53. What is the smallest of them?
  38. 38.The length of a rectangle is 6 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  39. 39.The length of a rectangle is 8 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  40. 40.Solve: 6(p − 5) = p + 50. What is p?

Answer key

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

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