Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 411 · 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(p − 2) = 2p + 4. What is p?
2. 2.Solve: 8p + 12 = 2p + 42. What is p?
3. 3.The length of a rectangle is 7 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
5. 5.The length of a rectangle is 8 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
6. 6.Solve: x/5 + x/2 = 42. What is x?
7. 7.Solve: 4(t − 1) = 2t + 8. What is t?
8. 8.A father is 9 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
9. 9.The sum of three consecutive whole numbers is 84. What is the largest of them?
10. 10.Solve: x/2 + x/3 = 15. What is x?
11. 11.The length of a rectangle is 14 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
12. 12.Solve: 3(m − 3) = m + 13. What is m?
13. 13.Solve: 9n + 8 = 7n + 22. What is n?
14. 14.Solve: 6p + 8 = 2p + 16. What is p?
15. 15.Solve: 5(t − 3) = t + 41. What is t?
16. 16.The sum of two consecutive whole numbers is 103. What is the smallest of them?
17. 17.The sum of four consecutive whole numbers is 146. What is the smallest of them?
18. 18.The length of a rectangle is 8 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
19. 19.Solve: t/6 + t/3 = 21. What is t?
20. 20.Solve: 6(n − 3) = 5n + 2. What is n?
21. 21.A father is 26 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?
22. 22.Solve: 3(n − 4) = n + 22. What is n?
23. 23.Solve: y/6 + y/3 = 18. What is y?
24. 24.The length of a rectangle is 2 cm more than its width. Its perimeter is 12 cm. What is its width (in cm)?
25. 25.A father is 12 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
26. 26.The sum of four consecutive whole numbers is 42. What is the smallest of them?
27. 27.Solve: 5x + 2 = 3x + 12. What is x?
28. 28.The sum of three consecutive whole numbers is 63. What is the smallest of them?
29. 29.Solve: 6(x − 1) = 5x + 9. What is x?
30. 30.The sum of four consecutive whole numbers is 238. What is the smallest of them?
31. 31.The sum of four consecutive whole numbers is 218. What is the largest of them?
32. 32.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?
33. 33.A father is 13 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
34. 34.Solve: n/3 + n/4 = 35. What is n?
35. 35.The length of a rectangle is 12 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
36. 36.Solve: 4(m − 5) = m + 10. What is m?
37. 37.A father is 32 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?
38. 38.Solve: 9m + 13 = m + 29. What is m?
39. 39.Solve: 3(x − 5) = x + 17. What is x?
40. 40.Solve: 5y + 5 = 3y + 35. What is y?

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