Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 677 · 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(p − 5) = 2p + 8. What is p?
2. 2.Solve: 7y + 3 = 2y + 13. What is y?
3. 3.Solve: 5(p − 2) = 4p + 5. What is p?
4. 4.The length of a rectangle is 3 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
5. 5.The sum of three consecutive whole numbers is 45. What is the smallest of them?
6. 6.Solve: m/4 + m/3 = 49. What is m?
7. 7.Solve: 7p + 5 = p + 41. What is p?
8. 8.Solve: y/5 + y/6 = 11. What is y?
9. 9.The sum of three consecutive whole numbers is 99. What is the smallest of them?
10. 10.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
11. 11.Solve: 3t + 7 = 2t + 13. What is t?
12. 12.Solve: 5(t − 5) = 2t + 20. What is t?
13. 13.A father is 6 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?
14. 14.A father is 13 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
15. 15.The sum of four consecutive whole numbers is 118. What is the largest of them?
16. 16.Solve: x/3 + x/5 = 32. What is x?
17. 17.A father is 9 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
18. 18.The sum of three consecutive whole numbers is 84. What is the largest of them?
19. 19.Solve: 6t + 13 = 3t + 49. What is t?
20. 20.The length of a rectangle is 12 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
21. 21.The length of a rectangle is 15 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
22. 22.The sum of two consecutive whole numbers is 65. What is the smallest of them?
23. 23.Solve: 3t + 19 = 2t + 22. What is t?
24. 24.Solve: 8x + 9 = 7x + 10. What is x?
25. 25.Solve: 8n + 4 = 7n + 10. What is n?
26. 26.A father is 14 years older than his son. In 5 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.A father is 10 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?
29. 29.The length of a rectangle is 10 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
30. 30.The sum of four consecutive whole numbers is 62. What is the largest of them?
31. 31.Solve: 4(t − 2) = 2t + 24. What is t?
32. 32.Solve: 6(x − 1) = 3x + 36. What is x?
33. 33.The length of a rectangle is 10 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
34. 34.A father is 39 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?
35. 35.The length of a rectangle is 13 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
36. 36.Solve: 4x + 15 = 2x + 19. What is x?
37. 37.Solve: 5(x − 3) = x + 21. What is x?
38. 38.Solve: 5y + 8 = y + 60. What is y?
39. 39.A father is 20 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?
40. 40.A father is 8 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?

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