Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 509 · 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 three consecutive whole numbers is 162. What is the smallest of them?
2. 2.The sum of three consecutive whole numbers is 96. What is the smallest of them?
3. 3.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?
4. 4.Solve: p/6 + p/3 = 18. What is p?
5. 5.Solve: t/3 + t/2 = 40. What is t?
6. 6.Solve: 9x + 19 = 2x + 117. What is x?
7. 7.Solve: 3(y − 4) = y + 26. What is y?
8. 8.The length of a rectangle is 11 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
9. 9.The length of a rectangle is 2 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
10. 10.The length of a rectangle is 4 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
11. 11.A father is 27 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?
12. 12.Solve: 6y + 7 = y + 32. What is y?
13. 13.The length of a rectangle is 1 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
14. 14.A father is 11 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
15. 15.Solve: x/4 + x/6 = 10. What is x?
16. 16.Solve: 5y + 18 = 3y + 20. What is y?
17. 17.The length of a rectangle is 3 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
18. 18.Solve: 4(t − 5) = t + 13. What is t?
19. 19.A father is 36 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?
20. 20.Solve: y/4 + y/2 = 24. What is y?
21. 21.Solve: 6m + 5 = 4m + 13. What is m?
22. 22.The length of a rectangle is 9 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
23. 23.Solve: 6(x − 4) = 4x + 22. What is x?
24. 24.Solve: 3(x − 2) = x + 4. What is x?
25. 25.The sum of two consecutive whole numbers is 93. What is the largest of them?
26. 26.Solve: 7y + 10 = 2y + 20. What is y?
27. 27.Solve: 5p + 11 = 2p + 41. What is p?
28. 28.Solve: 4(n − 5) = n + 28. What is n?
29. 29.A father is 15 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
30. 30.Solve: y/3 + y/6 = 9. What is y?
31. 31.Solve: n/6 + n/4 = 5. What is n?
32. 32.The sum of three consecutive whole numbers is 63. What is the smallest of them?
33. 33.The length of a rectangle is 7 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
34. 34.The sum of two consecutive whole numbers is 75. What is the largest of them?
35. 35.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
36. 36.The sum of four consecutive whole numbers is 230. What is the smallest of them?
37. 37.The sum of four consecutive whole numbers is 166. What is the smallest of them?
38. 38.The sum of four consecutive whole numbers is 30. What is the smallest of them?
39. 39.Solve: 8t + 18 = 5t + 54. What is t?
40. 40.The length of a rectangle is 5 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?

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