Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 313 · 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 6 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
2. 2.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
3. 3.Solve: 9n + 1 = 5n + 21. What is n?
4. 4.A father is 42 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?
5. 5.Solve: 6y + 11 = 5y + 21. What is y?
6. 6.Solve: 6m + 12 = 2m + 60. What is m?
7. 7.The length of a rectangle is 10 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
8. 8.Solve: 8y + 20 = 7y + 31. What is y?
9. 9.The sum of three consecutive whole numbers is 66. What is the smallest of them?
10. 10.The sum of two consecutive whole numbers is 37. What is the largest of them?
11. 11.The sum of three consecutive whole numbers is 78. What is the smallest of them?
12. 12.A father is 36 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?
13. 13.Solve: 3(p − 4) = p + 26. What is p?
14. 14.Solve: 6(x − 2) = 4x + 12. What is x?
15. 15.A father is 7 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
16. 16.Solve: 6p + 12 = 5p + 16. What is p?
17. 17.Solve: y/6 + y/3 = 15. What is y?
18. 18.The length of a rectangle is 15 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
19. 19.Solve: 5(y − 3) = 4y + 2. What is y?
20. 20.A father is 30 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?
21. 21.Solve: 7t + 20 = 6t + 35. What is t?
22. 22.Solve: 5(y − 4) = 2y + 28. What is y?
23. 23.Solve: 4y + 4 = y + 10. What is y?
24. 24.Solve: 3(x − 3) = 2x + 12. What is x?
25. 25.Solve: 6t + 15 = t + 25. What is t?
26. 26.A father is 15 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
27. 27.Solve: 5(m − 4) = m + 4. What is m?
28. 28.The sum of three consecutive whole numbers is 33. What is the smallest of them?
29. 29.Solve: 6x + 4 = x + 69. What is x?
30. 30.The sum of three consecutive whole numbers is 108. What is the smallest of them?
31. 31.The length of a rectangle is 9 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
32. 32.Solve: 3n + 12 = n + 30. What is n?
33. 33.The length of a rectangle is 2 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
34. 34.The sum of four consecutive whole numbers is 202. What is the smallest of them?
35. 35.Solve: 4p + 16 = p + 55. What is p?
36. 36.Solve: 6n + 18 = 5n + 21. What is n?
37. 37.Solve: 5(y − 2) = 3y + 12. What is y?
38. 38.The length of a rectangle is 13 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
39. 39.The length of a rectangle is 12 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
40. 40.Solve: 9n + 18 = 4n + 28. What is n?

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