Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 985 · 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 four consecutive whole numbers is 198. What is the smallest of them?
2. 2.Solve: 3(m − 4) = m + 8. What is m?
3. 3.The sum of three consecutive whole numbers is 54. What is the largest of them?
4. 4.The sum of three consecutive whole numbers is 21. What is the smallest of them?
5. 5.The sum of two consecutive whole numbers is 13. What is the smallest of them?
6. 6.Solve: 4(x − 1) = 3x + 2. What is x?
7. 7.The length of a rectangle is 6 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
8. 8.Solve: 9y + 1 = 5y + 61. What is y?
9. 9.Solve: m/6 + m/3 = 12. What is m?
10. 10.Solve: 8n + 6 = n + 41. What is n?
11. 11.The length of a rectangle is 11 cm more than its width. Its perimeter is 142 cm. What is its width (in cm)?
12. 12.Solve: 6(x − 3) = 4x + 22. What is x?
13. 13.A father is 6 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
14. 14.Solve: 3t + 3 = 2t + 15. What is t?
15. 15.Solve: 3(t − 4) = t + 24. What is t?
16. 16.Solve: 9p + 13 = 2p + 83. What is p?
17. 17.A father is 22 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?
18. 18.Solve: n/3 + n/4 = 42. What is n?
19. 19.A father is 9 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?
20. 20.Solve: 5(y − 4) = 3y + 20. What is y?
21. 21.Solve: 9x + 16 = 4x + 66. What is x?
22. 22.A father is 10 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
23. 23.Solve: 6(y − 4) = 2y + 24. What is y?
24. 24.The length of a rectangle is 1 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
25. 25.The length of a rectangle is 12 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
26. 26.Solve: y/2 + y/6 = 12. What is y?
27. 27.The length of a rectangle is 8 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
28. 28.Solve: p/5 + p/6 = 66. What is p?
29. 29.The length of a rectangle is 4 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
30. 30.The sum of four consecutive whole numbers is 102. What is the smallest of them?
31. 31.A father is 24 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
32. 32.Solve: 3(m − 2) = m + 4. What is m?
33. 33.Solve: 4(p − 1) = 2p + 4. What is p?
34. 34.Solve: 5x + 19 = 3x + 47. What is x?
35. 35.Solve: n/6 + n/5 = 55. What is n?
36. 36.A father is 18 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?
37. 37.Solve: p/2 + p/5 = 56. What is p?
38. 38.The sum of three consecutive whole numbers is 150. What is the smallest of them?
39. 39.A father is 20 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?
40. 40.Solve: 9n + 11 = 4n + 86. What is n?

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