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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 355 · 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.The sum of three consecutive whole numbers is 66. What is the smallest of them?
  2. 2.The sum of four consecutive whole numbers is 106. What is the smallest of them?
  3. 3.Solve: 4p + 9 = 3p + 13. What is p?
  4. 4.A father is 11 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  5. 5.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?
  6. 6.The length of a rectangle is 3 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  7. 7.Solve: 4p + 4 = p + 34. What is p?
  8. 8.Solve: 5(p − 1) = 2p + 16. What is p?
  9. 9.Solve: 3(p − 1) = p + 7. What is p?
  10. 10.Solve: 6(p − 3) = 2p + 50. What is p?
  11. 11.Solve: x/6 + x/3 = 18. What is x?
  12. 12.The length of a rectangle is 1 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  13. 13.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  14. 14.Solve: 5p + 3 = 3p + 11. What is p?
  15. 15.The sum of three consecutive whole numbers is 138. What is the largest of them?
  16. 16.The sum of two consecutive whole numbers is 107. What is the smallest of them?
  17. 17.Solve: 6(t − 1) = 4t + 18. What is t?
  18. 18.Solve: 4m + 11 = m + 35. What is m?
  19. 19.Solve: 5(t − 4) = 3t + 18. What is t?
  20. 20.Solve: 4(m − 3) = 3m + 12. What is m?
  21. 21.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  22. 22.Solve: t/5 + t/3 = 8. What is t?
  23. 23.Solve: m/3 + m/5 = 24. What is m?
  24. 24.Solve: t/2 + t/4 = 18. What is t?
  25. 25.The length of a rectangle is 7 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  26. 26.Solve: y/4 + y/2 = 6. What is y?
  27. 27.Solve: n/6 + n/2 = 20. What is n?
  28. 28.Solve: 4(y − 5) = y + 22. What is y?
  29. 29.A father is 45 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  30. 30.A father is 26 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?
  31. 31.A father is 24 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  32. 32.The length of a rectangle is 8 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  33. 33.Solve: 3(t − 1) = t + 7. What is t?
  34. 34.Solve: 7x + 9 = 4x + 51. What is x?
  35. 35.A father is 42 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?
  36. 36.Solve: 6y + 5 = 5y + 18. What is y?
  37. 37.Solve: m/4 + m/5 = 9. What is m?
  38. 38.Solve: m/4 + m/5 = 18. What is m?
  39. 39.The length of a rectangle is 13 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  40. 40.Solve: 8x + 20 = 2x + 38. What is x?

Answer key

  1. 21
  2. 25
  3. 4
  4. 4
  5. 2
  6. 25
  7. 10
  8. 7
  9. 5
  10. 17
  11. 36
  12. 9
  13. 8
  14. 4
  15. 47
  16. 53
  17. 12
  18. 8
  19. 19
  20. 24
  21. 11
  22. 15
  23. 45
  24. 24
  25. 4
  26. 8
  27. 30
  28. 14
  29. 10
  30. 8
  31. 9
  32. 7
  33. 5
  34. 14
  35. 12
  36. 13
  37. 20
  38. 40
  39. 20
  40. 3

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