Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 814 · 40 sums

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.

1. 1.The sum of two consecutive whole numbers is 27. What is the smallest of them?
2. 2.The sum of four consecutive whole numbers is 54. What is the largest of them?
3. 3.Solve: 3(t − 4) = t + 18. What is t?
4. 4.Solve: y/2 + y/3 = 30. What is y?
5. 5.A father is 28 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?
6. 6.The sum of three consecutive whole numbers is 126. What is the smallest of them?
7. 7.Solve: 5x + 19 = 3x + 49. What is x?
8. 8.The length of a rectangle is 14 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
9. 9.The length of a rectangle is 1 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
10. 10.Solve: 8t + 5 = 4t + 61. What is t?
11. 11.Solve: 3n + 17 = n + 37. What is n?
12. 12.A father is 24 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?
13. 13.Solve: p/2 + p/3 = 40. What is p?
14. 14.Solve: 4(y − 2) = y + 1. What is y?
15. 15.Solve: 6(x − 4) = x + 61. What is x?
16. 16.The sum of four consecutive whole numbers is 150. What is the largest of them?
17. 17.Solve: 5(y − 3) = 3y + 17. What is y?
18. 18.A father is 5 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
19. 19.Solve: 5(n − 5) = 2n + 26. What is n?
20. 20.Solve: 6y + 4 = 3y + 46. What is y?
21. 21.Solve: 6(n − 3) = 2n + 2. What is n?
22. 22.Solve: 6n + 8 = 3n + 53. What is n?
23. 23.Solve: 7x + 12 = 5x + 34. What is x?
24. 24.A father is 39 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?
25. 25.A father is 13 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
26. 26.Solve: 3x + 10 = 2x + 13. What is x?
27. 27.Solve: 6n + 14 = 5n + 17. What is n?
28. 28.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
29. 29.Solve: 8m + 14 = 3m + 74. What is m?
30. 30.The sum of two consecutive whole numbers is 43. What is the smallest of them?
31. 31.A father is 27 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
32. 32.The sum of two consecutive whole numbers is 59. What is the smallest of them?
33. 33.The sum of two consecutive whole numbers is 101. What is the smallest of them?
34. 34.Solve: t/2 + t/5 = 21. What is t?
35. 35.Solve: 6m + 14 = 3m + 29. What is m?
36. 36.A father is 13 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
37. 37.Solve: 6(t − 2) = 4t + 2. What is t?
38. 38.Solve: p/2 + p/6 = 12. What is p?
39. 39.A father is 9 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
40. 40.The length of a rectangle is 12 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?

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