Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 356 · 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 length of a rectangle is 10 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
2. 2.Solve: 7y + 20 = 3y + 68. What is y?
3. 3.The length of a rectangle is 12 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
4. 4.A father is 57 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?
5. 5.A father is 16 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
6. 6.The length of a rectangle is 3 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
7. 7.A father is 14 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?
8. 8.Solve: 6t + 1 = 5t + 10. What is t?
9. 9.The length of a rectangle is 1 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
10. 10.Solve: 5(y − 3) = 4y + 10. What is y?
11. 11.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?
12. 12.A father is 12 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?
13. 13.Solve: 5(y − 1) = 2y + 28. What is y?
14. 14.Solve: 5(x − 3) = x + 29. What is x?
15. 15.Solve: 5p + 2 = p + 42. What is p?
16. 16.Solve: p/5 + p/6 = 11. What is p?
17. 17.A father is 8 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?
18. 18.Solve: 3(x − 2) = x + 22. What is x?
19. 19.Solve: 4(x − 5) = x + 28. What is x?
20. 20.The sum of two consecutive whole numbers is 27. What is the largest of them?
21. 21.Solve: 7x + 1 = 5x + 25. What is x?
22. 22.Solve: y/3 + y/2 = 25. What is y?
23. 23.Solve: 4(p − 2) = 3p + 10. What is p?
24. 24.The length of a rectangle is 9 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
25. 25.The sum of three consecutive whole numbers is 84. What is the smallest of them?
26. 26.Solve: p/3 + p/5 = 64. What is p?
27. 27.Solve: 8n + 8 = 2n + 14. What is n?
28. 28.The sum of four consecutive whole numbers is 158. What is the smallest of them?
29. 29.Solve: 6m + 15 = 5m + 16. What is m?
30. 30.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: n/2 + n/3 = 40. What is n?
32. 32.Solve: m/2 + m/4 = 21. What is m?
33. 33.Solve: 3(x − 4) = x + 24. What is x?
34. 34.Solve: y/6 + y/5 = 66. What is y?
35. 35.Solve: y/2 + y/3 = 25. What is y?
36. 36.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?
37. 37.Solve: 6(x − 4) = 4x + 20. What is x?
38. 38.Solve: p/6 + p/2 = 12. 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 sum of three consecutive whole numbers is 114. What is the smallest of them?

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