Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 342 · 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.The sum of two consecutive whole numbers is 31. What is the largest of them?
2. 2.Solve: y/6 + y/4 = 10. What is y?
3. 3.Solve: 4(m − 2) = 2m + 4. What is m?
4. 4.Solve: n/5 + n/2 = 14. What is n?
5. 5.Solve: 5(p − 2) = 4p + 3. What is p?
6. 6.Solve: n/2 + n/4 = 6. What is n?
7. 7.The sum of two consecutive whole numbers is 47. What is the smallest of them?
8. 8.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?
9. 9.Solve: 3y + 7 = 2y + 22. What is y?
10. 10.Solve: 5(p − 4) = 4p + 4. What is p?
11. 11.Solve: 6x + 18 = 2x + 22. What is x?
12. 12.Solve: 8m + 12 = m + 117. What is m?
13. 13.Solve: 3(t − 3) = 2t + 2. What is t?
14. 14.The sum of four consecutive whole numbers is 78. What is the largest of them?
15. 15.A father is 30 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?
16. 16.Solve: 9t + 13 = 3t + 43. What is t?
17. 17.Solve: 9y + 17 = 4y + 77. What is y?
18. 18.The length of a rectangle is 4 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
19. 19.The length of a rectangle is 6 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
20. 20.Solve: 4t + 19 = 2t + 21. What is t?
21. 21.The length of a rectangle is 2 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
22. 22.The sum of four consecutive whole numbers is 58. What is the smallest of them?
23. 23.Solve: 6(t − 1) = t + 59. What is t?
24. 24.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?
25. 25.The sum of four consecutive whole numbers is 126. What is the smallest of them?
26. 26.A father is 27 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
27. 27.Solve: 3(y − 2) = 2y + 12. What is y?
28. 28.Solve: 6y + 4 = 3y + 13. What is y?
29. 29.The sum of four consecutive whole numbers is 218. What is the largest of them?
30. 30.Solve: 3(t − 4) = 2t + 10. What is t?
31. 31.Solve: n/5 + n/2 = 7. What is n?
32. 32.The sum of two consecutive whole numbers is 41. What is the largest of them?
33. 33.The length of a rectangle is 2 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
34. 34.A father is 30 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?
35. 35.A father is 12 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?
36. 36.The sum of three consecutive whole numbers is 111. What is the largest of them?
37. 37.Solve: 3(p − 4) = p + 24. What is p?
38. 38.Solve: 3(p − 1) = 2p + 13. What is p?
39. 39.The length of a rectangle is 3 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
40. 40.The length of a rectangle is 11 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?

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