Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 10 · 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 = 12. What is y?
2. 2.The sum of two consecutive whole numbers is 17. What is the largest of them?
3. 3.Solve: x/2 + x/4 = 24. What is x?
4. 4.Solve: y/5 + y/3 = 56. What is y?
5. 5.The length of a rectangle is 6 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
6. 6.Solve: y/5 + y/4 = 72. What is y?
7. 7.A father is 10 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
8. 8.Solve: x/3 + x/5 = 8. What is x?
9. 9.Solve: t/2 + t/5 = 21. What is t?
10. 10.Solve: 3m + 1 = m + 9. What is m?
11. 11.Solve: 3(n − 5) = 2n + 4. What is n?
12. 12.The sum of two consecutive whole numbers is 95. What is the largest of them?
13. 13.The length of a rectangle is 15 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
14. 14.Solve: 4(n − 4) = n + 23. What is n?
15. 15.Solve: 4(y − 1) = y + 2. What is y?
16. 16.Solve: 3p + 18 = p + 42. What is p?
17. 17.Solve: n/5 + n/3 = 16. What is n?
18. 18.Solve: 6x + 8 = 3x + 35. What is x?
19. 19.The sum of four consecutive whole numbers is 122. What is the smallest of them?
20. 20.Solve: 7y + 1 = y + 79. What is y?
21. 21.Solve: t/5 + t/4 = 45. What is t?
22. 22.Solve: 5x + 7 = 4x + 20. What is x?
23. 23.Solve: 8y + 10 = 7y + 15. What is y?
24. 24.Solve: t/5 + t/3 = 64. What is t?
25. 25.The sum of two consecutive whole numbers is 103. What is the smallest of them?
26. 26.A father is 54 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
27. 27.The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
28. 28.A father is 12 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?
29. 29.Solve: 3(y − 5) = y + 7. What is y?
30. 30.The length of a rectangle is 1 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
31. 31.The length of a rectangle is 8 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
32. 32.A father is 20 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?
33. 33.A father is 18 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?
34. 34.A father is 18 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?
35. 35.Solve: n/2 + n/3 = 25. What is n?
36. 36.The length of a rectangle is 3 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
37. 37.The length of a rectangle is 8 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
38. 38.Solve: 5t + 13 = 3t + 33. What is t?
39. 39.A father is 30 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
40. 40.Solve: 3(y − 3) = y + 7. What is y?

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