Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 482 · 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: n/2 + n/4 = 9. What is n?
2. 2.Solve: p/6 + p/2 = 32. What is p?
3. 3.Solve: p/5 + p/3 = 16. What is p?
4. 4.The sum of two consecutive whole numbers is 83. What is the smallest of them?
5. 5.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
6. 6.The length of a rectangle is 15 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
7. 7.The length of a rectangle is 14 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
8. 8.Solve: 3(m − 1) = m + 13. What is m?
9. 9.Solve: 3n + 18 = 2n + 32. What is n?
10. 10.The sum of three consecutive whole numbers is 54. What is the smallest of them?
11. 11.Solve: 4(p − 5) = 2p + 2. What is p?
12. 12.The length of a rectangle is 10 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
13. 13.A father is 30 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
14. 14.Solve: 3x + 1 = 2x + 15. What is x?
15. 15.Solve: y/5 + y/6 = 44. What is y?
16. 16.Solve: x/6 + x/5 = 55. What is x?
17. 17.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?
18. 18.A father is 42 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
19. 19.The length of a rectangle is 15 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
20. 20.Solve: n/2 + n/6 = 16. What is n?
21. 21.A father is 5 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
22. 22.Solve: 4x + 1 = 3x + 10. What is x?
23. 23.Solve: 8y + 9 = 3y + 54. What is y?
24. 24.The sum of two consecutive whole numbers is 77. What is the largest of them?
25. 25.The sum of three consecutive whole numbers is 75. What is the largest of them?
26. 26.Solve: 3(n − 5) = 2n + 9. What is n?
27. 27.Solve: 5(p − 3) = p + 29. What is p?
28. 28.A father is 42 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?
29. 29.Solve: 3x + 1 = x + 7. What is x?
30. 30.Solve: x/6 + x/3 = 15. What is x?
31. 31.The sum of three consecutive whole numbers is 153. What is the smallest of them?
32. 32.Solve: 4p + 10 = 3p + 13. What is p?
33. 33.Solve: 3x + 20 = x + 42. What is x?
34. 34.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
35. 35.The length of a rectangle is 7 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
36. 36.The length of a rectangle is 3 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
37. 37.Solve: 6(n − 5) = 5n + 9. What is n?
38. 38.A father is 13 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
39. 39.The length of a rectangle is 3 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
40. 40.A father is 17 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?

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