Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 88 · 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: 6(t − 2) = 3t + 3. What is t?
2. 2.The sum of three consecutive whole numbers is 54. What is the largest of them?
3. 3.The length of a rectangle is 15 cm more than its width. Its perimeter is 142 cm. What is its width (in cm)?
4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
5. 5.Solve: 8x + 20 = 4x + 64. What is x?
6. 6.Solve: 9n + 4 = 5n + 64. What is n?
7. 7.A father is 24 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?
8. 8.Solve: 6(n − 3) = n + 27. What is n?
9. 9.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
10. 10.The sum of three consecutive whole numbers is 162. What is the smallest of them?
11. 11.The length of a rectangle is 1 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
12. 12.Solve: y/2 + y/5 = 49. What is y?
13. 13.The length of a rectangle is 5 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
14. 14.Solve: 6(y − 1) = 3y + 36. What is y?
15. 15.Solve: 5(t − 3) = 4t + 1. What is t?
16. 16.The length of a rectangle is 7 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
17. 17.Solve: n/2 + n/4 = 6. What is n?
18. 18.Solve: 5x + 10 = 4x + 12. What is x?
19. 19.Solve: y/2 + y/4 = 18. What is y?
20. 20.Solve: 7n + 6 = 5n + 26. What is n?
21. 21.A father is 20 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?
22. 22.Solve: p/2 + p/3 = 15. What is p?
23. 23.The sum of two consecutive whole numbers is 99. What is the smallest of them?
24. 24.Solve: m/2 + m/6 = 12. What is m?
25. 25.A father is 51 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?
26. 26.Solve: x/6 + x/2 = 32. What is x?
27. 27.The length of a rectangle is 3 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
28. 28.Solve: x/6 + x/3 = 6. What is x?
29. 29.Solve: 6(n − 3) = n + 32. What is n?
30. 30.The sum of three consecutive whole numbers is 183. What is the smallest of them?
31. 31.The sum of three consecutive whole numbers is 69. What is the smallest of them?
32. 32.Solve: 5(p − 2) = 4p + 8. What is p?
33. 33.Solve: 3(p − 1) = p + 3. What is p?
34. 34.The length of a rectangle is 4 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
35. 35.The sum of four consecutive whole numbers is 90. What is the largest of them?
36. 36.The sum of four consecutive whole numbers is 142. What is the smallest of them?
37. 37.Solve: p/4 + p/3 = 21. What is p?
38. 38.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
39. 39.The length of a rectangle is 8 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
40. 40.A father is 30 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?

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