Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 61 · 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.Solve: 3(p − 1) = 2p + 4. What is p?
2. 2.Solve: 3n + 5 = n + 9. What is n?
3. 3.Solve: 5(m − 5) = 2m + 17. What is m?
4. 4.A father is 10 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?
5. 5.Solve: 3(x − 5) = x + 7. What is x?
6. 6.The sum of three consecutive whole numbers is 51. What is the smallest of them?
7. 7.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
8. 8.Solve: t/4 + t/3 = 21. What is t?
9. 9.Solve: 5(t − 5) = 4t + 8. What is t?
10. 10.The sum of four consecutive whole numbers is 86. What is the largest of them?
11. 11.Solve: 8p + 15 = 7p + 19. What is p?
12. 12.A father is 36 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?
13. 13.A father is 24 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?
14. 14.A father is 13 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
15. 15.Solve: 9y + 13 = 4y + 73. What is y?
16. 16.Solve: 6n + 9 = 4n + 35. What is n?
17. 17.The sum of four consecutive whole numbers is 162. What is the smallest of them?
18. 18.Solve: 7n + 15 = 2n + 25. What is n?
19. 19.Solve: p/4 + p/3 = 42. What is p?
20. 20.Solve: 4x + 10 = 3x + 25. What is x?
21. 21.Solve: 9y + 13 = 2y + 62. What is y?
22. 22.The length of a rectangle is 5 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
23. 23.The sum of two consecutive whole numbers is 29. What is the largest of them?
24. 24.A father is 16 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?
25. 25.A father is 42 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?
26. 26.Solve: 5y + 12 = 3y + 24. What is y?
27. 27.Solve: 9y + 5 = 3y + 23. What is y?
28. 28.The length of a rectangle is 5 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
29. 29.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?
30. 30.A father is 17 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: 3(p − 1) = p + 23. What is p?
32. 32.Solve: 9m + 14 = 5m + 54. What is m?
33. 33.Solve: 6(m − 2) = 2m + 36. What is m?
34. 34.The length of a rectangle is 5 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
35. 35.The sum of two consecutive whole numbers is 43. What is the smallest of them?
36. 36.A father is 14 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?
37. 37.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?
38. 38.Solve: 3(y − 1) = y + 21. What is y?
39. 39.Solve: 5(t − 3) = 4t + 4. What is t?
40. 40.The length of a rectangle is 12 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?

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