Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 333 · 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 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
2. 2.Solve: 6(t − 3) = 3t + 27. What is t?
3. 3.A father is 27 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?
4. 4.The sum of four consecutive whole numbers is 66. What is the smallest of them?
5. 5.A father is 16 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
6. 6.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
7. 7.Solve: 6(n − 1) = n + 19. What is n?
8. 8.Solve: 3(n − 1) = n + 1. What is n?
9. 9.Solve: y/6 + y/3 = 24. What is y?
10. 10.Solve: 9p + 18 = 2p + 46. What is p?
11. 11.The length of a rectangle is 8 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
12. 12.The length of a rectangle is 11 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
13. 13.Solve: 3t + 9 = 2t + 18. What is t?
14. 14.Solve: t/4 + t/3 = 14. What is t?
15. 15.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
16. 16.The sum of three consecutive whole numbers is 147. What is the largest of them?
17. 17.Solve: 6n + 15 = 4n + 33. What is n?
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 26 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
20. 20.Solve: y/2 + y/3 = 40. What is y?
21. 21.The sum of three consecutive whole numbers is 153. What is the smallest of them?
22. 22.Solve: 5(p − 2) = 4p + 10. What is p?
23. 23.Solve: x/6 + x/4 = 15. What is x?
24. 24.The length of a rectangle is 9 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
25. 25.A father is 27 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?
26. 26.Solve: 4(m − 5) = m + 1. What is m?
27. 27.Solve: t/3 + t/5 = 56. What is t?
28. 28.Solve: x/2 + x/4 = 12. What is x?
29. 29.Solve: p/4 + p/2 = 15. What is p?
30. 30.The length of a rectangle is 12 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
31. 31.The length of a rectangle is 3 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
32. 32.The sum of two consecutive whole numbers is 107. What is the largest of them?
33. 33.Solve: m/4 + m/5 = 45. What is m?
34. 34.Solve: 5x + 9 = 2x + 27. What is x?
35. 35.A father is 18 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
36. 36.Solve: y/2 + y/6 = 16. What is y?
37. 37.The length of a rectangle is 12 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
38. 38.Solve: x/2 + x/4 = 18. What is x?
39. 39.A father is 6 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
40. 40.The length of a rectangle is 1 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?

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