Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 109 · 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: 6y + 5 = 5y + 11. What is y?
2. 2.The sum of two consecutive whole numbers is 45. What is the largest of them?
3. 3.The sum of two consecutive whole numbers is 53. What is the largest of them?
4. 4.The sum of two consecutive whole numbers is 13. What is the largest of them?
5. 5.The sum of three consecutive whole numbers is 75. What is the smallest of them?
6. 6.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?
7. 7.The sum of four consecutive whole numbers is 54. What is the smallest of them?
8. 8.The sum of four consecutive whole numbers is 38. What is the smallest of them?
9. 9.The sum of four consecutive whole numbers is 158. What is the smallest of them?
10. 10.Solve: t/5 + t/2 = 42. What is t?
11. 11.Solve: 4(x − 4) = x + 17. What is x?
12. 12.Solve: 6p + 4 = p + 9. What is p?
13. 13.Solve: 8t + 7 = 3t + 12. What is t?
14. 14.The sum of three consecutive whole numbers is 165. What is the largest of them?
15. 15.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?
16. 16.Solve: 5(n − 2) = 3n + 18. What is n?
17. 17.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
18. 18.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
19. 19.The sum of three consecutive whole numbers is 60. What is the smallest of them?
20. 20.A father is 30 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
21. 21.The sum of three consecutive whole numbers is 36. What is the largest of them?
22. 22.The length of a rectangle is 5 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
23. 23.Solve: 5(y − 1) = y + 11. What is y?
24. 24.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?
25. 25.The length of a rectangle is 11 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
26. 26.A father is 16 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
27. 27.The sum of three consecutive whole numbers is 45. What is the largest of them?
28. 28.The sum of three consecutive whole numbers is 147. What is the smallest of them?
29. 29.A father is 27 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
30. 30.Solve: 8y + 8 = 5y + 17. What is y?
31. 31.Solve: 4(n − 2) = 3n + 11. What is n?
32. 32.The sum of four consecutive whole numbers is 66. What is the smallest of them?
33. 33.The sum of two consecutive whole numbers is 27. What is the largest of them?
34. 34.The sum of four consecutive whole numbers is 174. What is the largest of them?
35. 35.Solve: m/6 + m/4 = 20. What is m?
36. 36.Solve: 4(n − 1) = 3n + 2. What is n?
37. 37.The sum of three consecutive whole numbers is 171. What is the smallest of them?
38. 38.A father is 11 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
39. 39.Solve: 3(x − 1) = x + 21. What is x?
40. 40.The length of a rectangle is 6 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?

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