Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 861 · 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 10 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?
2. 2.Solve: 7t + 17 = 2t + 57. What is t?
3. 3.The length of a rectangle is 10 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
4. 4.Solve: 4(t − 1) = t + 35. What is t?
5. 5.Solve: 9x + 9 = 4x + 59. What is x?
6. 6.A father is 9 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
7. 7.Solve: 8p + 4 = 4p + 8. What is p?
8. 8.Solve: 8p + 5 = 2p + 89. What is p?
9. 9.A father is 14 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
10. 10.Solve: 5(y − 5) = 4y + 10. What is y?
11. 11.Solve: 4(m − 1) = 2m + 16. What is m?
12. 12.A father is 20 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?
13. 13.The sum of two consecutive whole numbers is 119. What is the smallest of them?
14. 14.The length of a rectangle is 2 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
15. 15.Solve: 3y + 10 = 2y + 18. What is y?
16. 16.Solve: 3p + 14 = 2p + 17. What is p?
17. 17.Solve: 8p + 2 = 5p + 8. What is p?
18. 18.The sum of two consecutive whole numbers is 85. What is the smallest of them?
19. 19.The length of a rectangle is 8 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
20. 20.Solve: 3(p − 1) = 2p + 6. What is p?
21. 21.A father is 11 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
22. 22.The sum of three consecutive whole numbers is 147. What is the smallest of them?
23. 23.A father is 15 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?
24. 24.The length of a rectangle is 12 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
25. 25.Solve: y/4 + y/2 = 18. What is y?
26. 26.Solve: 3x + 3 = x + 13. What is x?
27. 27.Solve: 3(x − 5) = x + 13. What is x?
28. 28.The length of a rectangle is 15 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
29. 29.The length of a rectangle is 7 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
30. 30.Solve: 3(y − 2) = y + 16. What is y?
31. 31.Solve: 3x + 15 = x + 17. What is x?
32. 32.Solve: p/4 + p/2 = 18. What is p?
33. 33.A father is 5 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
34. 34.The sum of two consecutive whole numbers is 97. What is the largest of them?
35. 35.The sum of two consecutive whole numbers is 107. What is the smallest of them?
36. 36.A father is 6 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
37. 37.The length of a rectangle is 9 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
38. 38.A father is 33 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?
39. 39.Solve: 8m + 15 = 6m + 25. What is m?
40. 40.The length of a rectangle is 12 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?

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