Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 436 · 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 length of a rectangle is 2 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
2. 2.The length of a rectangle is 8 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
3. 3.The length of a rectangle is 8 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
4. 4.Solve: 3(x − 1) = x + 3. What is x?
5. 5.Solve: 5(y − 4) = 3y + 20. What is y?
6. 6.Solve: 9n + 19 = 8n + 22. What is n?
7. 7.A father is 26 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
8. 8.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
9. 9.The length of a rectangle is 8 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
10. 10.The sum of three consecutive whole numbers is 66. What is the largest of them?
11. 11.Solve: n/3 + n/5 = 48. What is n?
12. 12.Solve: 4y + 7 = 3y + 10. What is y?
13. 13.The length of a rectangle is 13 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
14. 14.The sum of three consecutive whole numbers is 162. What is the largest of them?
15. 15.A father is 15 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
16. 16.Solve: 4(x − 2) = x + 1. What is x?
17. 17.Solve: 3(x − 5) = x + 7. What is x?
18. 18.Solve: 4n + 11 = 3n + 18. What is n?
19. 19.Solve: 3(m − 4) = 2m + 1. What is m?
20. 20.The sum of two consecutive whole numbers is 117. What is the smallest of them?
21. 21.Solve: 5(n − 3) = 3n + 5. What is n?
22. 22.A father is 28 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?
23. 23.A father is 9 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
24. 24.Solve: 4m + 7 = m + 16. What is m?
25. 25.Solve: 4n + 11 = n + 32. What is n?
26. 26.A father is 19 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
27. 27.The length of a rectangle is 3 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
28. 28.Solve: 5(t − 3) = 2t + 27. What is t?
29. 29.Solve: 9x + 15 = 7x + 21. What is x?
30. 30.Solve: t/3 + t/4 = 14. What is t?
31. 31.Solve: 6(t − 1) = t + 54. What is t?
32. 32.The sum of three consecutive whole numbers is 84. What is the smallest of them?
33. 33.The length of a rectangle is 10 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
34. 34.The sum of two consecutive whole numbers is 103. What is the largest of them?
35. 35.A father is 45 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
36. 36.A father is 39 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?
37. 37.Solve: 4(n − 2) = n + 16. What is n?
38. 38.Solve: 6y + 4 = 2y + 20. What is y?
39. 39.A father is 12 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?
40. 40.Solve: 3y + 11 = 2y + 15. What is y?

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