Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 855 · 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(y − 3) = 2y + 12. What is y?
2. 2.Solve: 3x + 12 = 2x + 18. What is x?
3. 3.The length of a rectangle is 13 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
4. 4.Solve: y/2 + y/6 = 32. What is y?
5. 5.Solve: 5(p − 5) = 3p + 25. What is p?
6. 6.Solve: 3y + 3 = y + 33. What is y?
7. 7.The sum of three consecutive whole numbers is 30. What is the smallest of them?
8. 8.The length of a rectangle is 10 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
9. 9.Solve: y/2 + y/4 = 21. What is y?
10. 10.A father is 57 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?
11. 11.A father is 20 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?
12. 12.The sum of three consecutive whole numbers is 87. What is the largest of them?
13. 13.The length of a rectangle is 5 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
14. 14.A father is 26 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?
15. 15.Solve: 8t + 16 = 2t + 28. What is t?
16. 16.Solve: 9x + 13 = 4x + 43. What is x?
17. 17.The sum of four consecutive whole numbers is 58. What is the smallest of them?
18. 18.The sum of four consecutive whole numbers is 82. What is the smallest of them?
19. 19.Solve: 5n + 9 = 2n + 18. What is n?
20. 20.A father is 8 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
21. 21.Solve: y/6 + y/3 = 9. What is y?
22. 22.Solve: 4p + 2 = 3p + 10. What is p?
23. 23.The sum of four consecutive whole numbers is 50. What is the largest of them?
24. 24.The sum of four consecutive whole numbers is 46. What is the largest of them?
25. 25.Solve: y/3 + y/4 = 49. What is y?
26. 26.A father is 51 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?
27. 27.Solve: 3(y − 2) = 2y + 10. What is y?
28. 28.Solve: 4(p − 5) = p + 19. What is p?
29. 29.Solve: t/3 + t/4 = 56. What is t?
30. 30.A father is 14 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?
31. 31.Solve: 8t + 8 = 5t + 11. What is t?
32. 32.The sum of three consecutive whole numbers is 159. What is the smallest of them?
33. 33.Solve: n/2 + n/3 = 10. What is n?
34. 34.The sum of three consecutive whole numbers is 150. What is the smallest of them?
35. 35.The length of a rectangle is 14 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
36. 36.The length of a rectangle is 7 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
37. 37.The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
38. 38.Solve: p/5 + p/3 = 64. What is p?
39. 39.The length of a rectangle is 3 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
40. 40.The sum of two consecutive whole numbers is 51. What is the smallest of them?

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