Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 577 · 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 39 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
2. 2.The sum of two consecutive whole numbers is 113. What is the smallest of them?
3. 3.Solve: p/2 + p/6 = 12. What is p?
4. 4.Solve: x/5 + x/4 = 9. What is x?
5. 5.The sum of three consecutive whole numbers is 54. What is the largest of them?
6. 6.The length of a rectangle is 7 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
7. 7.Solve: 3(x − 2) = x + 22. What is x?
8. 8.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
9. 9.Solve: 4(y − 1) = y + 8. What is y?
10. 10.Solve: 5(m − 5) = 4m + 1. What is m?
11. 11.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?
12. 12.Solve: 3(m − 3) = m + 17. What is m?
13. 13.Solve: x/2 + x/3 = 35. What is x?
14. 14.A father is 28 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?
15. 15.Solve: 9n + 11 = n + 51. What is n?
16. 16.Solve: x/3 + x/6 = 12. What is x?
17. 17.Solve: 5(y − 3) = 2y + 12. What is y?
18. 18.A father is 57 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?
19. 19.Solve: x/3 + x/2 = 35. What is x?
20. 20.The length of a rectangle is 2 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
21. 21.A father is 36 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?
22. 22.The length of a rectangle is 11 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
23. 23.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?
24. 24.The sum of two consecutive whole numbers is 111. What is the smallest of them?
25. 25.The sum of four consecutive whole numbers is 170. What is the largest of them?
26. 26.The sum of three consecutive whole numbers is 183. What is the smallest of them?
27. 27.Solve: y/3 + y/6 = 12. What is y?
28. 28.A father is 14 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
29. 29.Solve: 7y + 20 = 3y + 40. What is y?
30. 30.Solve: 4(x − 5) = 2x + 10. What is x?
31. 31.Solve: 3(n − 1) = n + 11. What is n?
32. 32.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
33. 33.Solve: 7y + 12 = 3y + 24. What is y?
34. 34.Solve: 3y + 11 = y + 15. What is y?
35. 35.Solve: x/6 + x/5 = 66. What is x?
36. 36.Solve: 3x + 17 = 2x + 18. What is x?
37. 37.Solve: 4m + 4 = m + 46. What is m?
38. 38.Solve: 6(t − 2) = t + 3. What is t?
39. 39.A father is 51 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?
40. 40.Solve: 9n + 9 = 6n + 15. What is n?

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