Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 706 · 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: 7x + 5 = 3x + 13. What is x?
2. 2.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?
3. 3.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?
4. 4.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?
5. 5.The length of a rectangle is 5 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
6. 6.Solve: 6(t − 4) = 2t + 20. What is t?
7. 7.A father is 18 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?
8. 8.The sum of three consecutive whole numbers is 180. What is the largest of them?
9. 9.The length of a rectangle is 5 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
10. 10.A father is 24 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?
11. 11.The length of a rectangle is 13 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
12. 12.The length of a rectangle is 7 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
13. 13.Solve: 8m + 8 = 2m + 68. What is m?
14. 14.The sum of two consecutive whole numbers is 71. What is the largest of them?
15. 15.Solve: 3(t − 4) = t + 10. What is t?
16. 16.A father is 33 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
17. 17.Solve: 6y + 11 = y + 46. What is y?
18. 18.Solve: m/6 + m/2 = 4. What is m?
19. 19.Solve: 5n + 6 = 4n + 19. What is n?
20. 20.Solve: 8x + 2 = 7x + 15. What is x?
21. 21.Solve: 5(x − 1) = 4x + 3. What is x?
22. 22.The sum of three consecutive whole numbers is 42. What is the smallest of them?
23. 23.The sum of three consecutive whole numbers is 96. What is the smallest of them?
24. 24.Solve: y/4 + y/6 = 25. What is y?
25. 25.The length of a rectangle is 4 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
26. 26.The sum of three consecutive whole numbers is 63. What is the smallest of them?
27. 27.A father is 51 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
28. 28.Solve: 4(x − 1) = 2x + 8. What is x?
29. 29.Solve: 5(x − 5) = 3x + 21. What is x?
30. 30.A father is 12 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
31. 31.The length of a rectangle is 15 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
32. 32.The sum of four consecutive whole numbers is 166. What is the smallest of them?
33. 33.The length of a rectangle is 10 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
34. 34.Solve: p/2 + p/4 = 6. What is p?
35. 35.Solve: 7t + 1 = 3t + 17. What is t?
36. 36.The length of a rectangle is 2 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
37. 37.Solve: x/3 + x/4 = 49. What is x?
38. 38.Solve: p/3 + p/5 = 64. What is p?
39. 39.The sum of two consecutive whole numbers is 39. What is the smallest of them?
40. 40.The sum of four consecutive whole numbers is 78. What is the smallest of them?

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