Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 116 · 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.Solve: y/6 + y/2 = 32. What is y?
2. 2.The length of a rectangle is 6 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
3. 3.Solve: 6(x − 1) = 4x + 8. What is x?
4. 4.Solve: 6(t − 5) = 3t + 39. What is t?
5. 5.Solve: 9t + 6 = 7t + 12. What is t?
6. 6.The sum of four consecutive whole numbers is 238. What is the largest of them?
7. 7.A father is 13 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
8. 8.The sum of two consecutive whole numbers is 69. What is the smallest of them?
9. 9.Solve: p/6 + p/5 = 11. What is p?
10. 10.Solve: 5(m − 3) = 4m + 4. What is m?
11. 11.The length of a rectangle is 10 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
12. 12.Solve: 4p + 2 = 3p + 10. What is p?
13. 13.Solve: x/2 + x/5 = 49. What is x?
14. 14.Solve: n/5 + n/2 = 21. What is n?
15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
16. 16.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?
17. 17.A father is 16 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?
18. 18.The sum of three consecutive whole numbers is 123. What is the smallest of them?
19. 19.Solve: p/5 + p/2 = 28. What is p?
20. 20.Solve: x/5 + x/3 = 24. What is x?
21. 21.Solve: 3(p − 1) = p + 17. What is p?
22. 22.A father is 26 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?
23. 23.The length of a rectangle is 6 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
24. 24.A father is 9 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
25. 25.The sum of two consecutive whole numbers is 57. What is the smallest of them?
26. 26.The length of a rectangle is 12 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
27. 27.Solve: x/6 + x/4 = 10. What is x?
28. 28.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?
29. 29.The sum of two consecutive whole numbers is 17. What is the largest of them?
30. 30.A father is 15 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: 8y + 12 = 3y + 67. What is y?
32. 32.A father is 32 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?
33. 33.The sum of two consecutive whole numbers is 53. What is the smallest of them?
34. 34.The length of a rectangle is 12 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
35. 35.The length of a rectangle is 15 cm more than its width. Its perimeter is 150 cm. What is its width (in cm)?
36. 36.Solve: 6(t − 2) = 5t + 4. What is t?
37. 37.A father is 13 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
38. 38.Solve: p/4 + p/6 = 15. What is p?
39. 39.The sum of two consecutive whole numbers is 97. What is the largest of them?
40. 40.The sum of three consecutive whole numbers is 141. What is the smallest of them?

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