Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 311 · 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 13 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
2. 2.Solve: x/5 + x/2 = 14. What is x?
3. 3.The length of a rectangle is 14 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
4. 4.The sum of four consecutive whole numbers is 162. What is the largest of them?
5. 5.Solve: 5t + 17 = 2t + 50. What is t?
6. 6.Solve: 5(m − 3) = 2m + 12. What is m?
7. 7.Solve: n/2 + n/3 = 15. What is n?
8. 8.A father is 30 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?
9. 9.Solve: 5(y − 2) = y + 14. What is y?
10. 10.Solve: 3(m − 5) = 2m + 6. What is m?
11. 11.A father is 18 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?
12. 12.Solve: y/5 + y/4 = 45. What is y?
13. 13.Solve: 5(n − 5) = 2n + 35. What is n?
14. 14.The length of a rectangle is 13 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
15. 15.A father is 34 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
16. 16.The sum of four consecutive whole numbers is 170. What is the smallest of them?
17. 17.A father is 39 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?
18. 18.A father is 20 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?
19. 19.A father is 28 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
20. 20.Solve: 8y + 16 = 7y + 28. What is y?
21. 21.The sum of two consecutive whole numbers is 61. What is the smallest of them?
22. 22.Solve: n/2 + n/3 = 30. What is n?
23. 23.The sum of three consecutive whole numbers is 42. What is the smallest of them?
24. 24.Solve: 4p + 12 = 2p + 28. What is p?
25. 25.Solve: 6y + 11 = 2y + 55. What is y?
26. 26.The sum of three consecutive whole numbers is 180. What is the smallest of them?
27. 27.The length of a rectangle is 7 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
28. 28.The sum of four consecutive whole numbers is 94. What is the largest of them?
29. 29.Solve: 3(x − 1) = x + 9. What is x?
30. 30.The length of a rectangle is 9 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
31. 31.Solve: t/3 + t/2 = 15. What is t?
32. 32.The sum of four consecutive whole numbers is 174. What is the largest of them?
33. 33.Solve: 5(y − 4) = y + 32. What is y?
34. 34.A father is 30 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?
35. 35.A father is 21 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?
36. 36.A father is 54 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?
37. 37.Solve: 4(y − 1) = y + 8. What is y?
38. 38.A father is 30 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?
39. 39.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
40. 40.Solve: 5p + 17 = 2p + 59. What is p?

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