Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 237 · 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 9 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
2. 2.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?
3. 3.Solve: 6(x − 2) = 4x + 2. What is x?
4. 4.Solve: 8y + 11 = 3y + 26. What is y?
5. 5.Solve: x/3 + x/2 = 40. What is x?
6. 6.Solve: p/6 + p/2 = 20. What is p?
7. 7.Solve: 4(m − 3) = 3m + 1. What is m?
8. 8.Solve: y/5 + y/3 = 48. What is y?
9. 9.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?
10. 10.The sum of three consecutive whole numbers is 117. What is the smallest of them?
11. 11.Solve: 6(y − 4) = 5y + 6. What is y?
12. 12.The length of a rectangle is 1 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
13. 13.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
14. 14.The sum of two consecutive whole numbers is 15. What is the smallest of them?
15. 15.The length of a rectangle is 15 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
16. 16.A father is 24 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?
17. 17.Solve: 6p + 17 = 3p + 44. What is p?
18. 18.Solve: 7n + 11 = 2n + 51. What is n?
19. 19.Solve: 6(y − 4) = 4y + 24. What is y?
20. 20.Solve: 7y + 9 = 2y + 79. What is y?
21. 21.Solve: 6n + 18 = 5n + 21. What is n?
22. 22.Solve: n/3 + n/4 = 7. What is n?
23. 23.The length of a rectangle is 5 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
24. 24.The sum of three consecutive whole numbers is 153. What is the smallest of them?
25. 25.Solve: 8x + 6 = x + 34. What is x?
26. 26.Solve: 5x + 13 = 4x + 24. What is x?
27. 27.Solve: 3y + 15 = y + 37. What is y?
28. 28.The sum of two consecutive whole numbers is 19. What is the largest of them?
29. 29.Solve: x/5 + x/2 = 14. What is x?
30. 30.A father is 42 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?
31. 31.A father is 24 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?
32. 32.The sum of two consecutive whole numbers is 11. What is the smallest of them?
33. 33.A father is 22 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?
34. 34.Solve: 5(y − 3) = 3y + 15. What is y?
35. 35.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
36. 36.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
37. 37.The sum of three consecutive whole numbers is 135. What is the smallest of them?
38. 38.Solve: 6p + 4 = 2p + 64. What is p?
39. 39.Solve: 3(t − 1) = t + 5. What is t?
40. 40.Solve: y/5 + y/3 = 16. What is y?

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