Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 410 · 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.A father is 21 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?
2. 2.The length of a rectangle is 3 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
3. 3.Solve: y/3 + y/2 = 20. What is y?
4. 4.The sum of four consecutive whole numbers is 82. What is the largest of them?
5. 5.Solve: 6p + 10 = 4p + 24. What is p?
6. 6.A father is 14 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?
7. 7.The sum of two consecutive whole numbers is 31. What is the largest of them?
8. 8.The length of a rectangle is 1 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
9. 9.Solve: x/3 + x/5 = 16. What is x?
10. 10.The length of a rectangle is 14 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
11. 11.The sum of four consecutive whole numbers is 50. What is the smallest of them?
12. 12.Solve: 5(n − 2) = 4n + 3. What is n?
13. 13.A father is 30 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?
14. 14.The length of a rectangle is 9 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
15. 15.The sum of three consecutive whole numbers is 144. What is the smallest of them?
16. 16.Solve: 9x + 8 = 2x + 78. What is x?
17. 17.Solve: 4p + 2 = 3p + 6. What is p?
18. 18.Solve: 3(t − 4) = 2t + 9. What is t?
19. 19.Solve: 4m + 15 = m + 48. What is m?
20. 20.Solve: y/2 + y/4 = 15. What is y?
21. 21.A father is 20 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?
22. 22.A father is 32 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?
23. 23.A father is 12 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
24. 24.The sum of two consecutive whole numbers is 25. What is the largest of them?
25. 25.The sum of four consecutive whole numbers is 238. What is the largest of them?
26. 26.Solve: 4x + 20 = x + 41. What is x?
27. 27.The sum of four consecutive whole numbers is 130. What is the smallest of them?
28. 28.Solve: 6(n − 2) = 2n + 4. What is n?
29. 29.Solve: t/6 + t/3 = 12. What is t?
30. 30.Solve: 6y + 8 = 4y + 38. What is y?
31. 31.Solve: 5(n − 3) = n + 41. What is n?
32. 32.Solve: x/6 + x/5 = 88. What is x?
33. 33.Solve: 3n + 3 = 2n + 7. What is n?
34. 34.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?
35. 35.Solve: t/5 + t/4 = 45. What is t?
36. 36.The length of a rectangle is 13 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
37. 37.Solve: y/5 + y/3 = 16. What is y?
38. 38.Solve: 5(y − 2) = y + 42. What is y?
39. 39.A father is 9 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
40. 40.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?

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