Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 329 · 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: m/3 + m/2 = 35. What is m?
2. 2.Solve: 3x + 18 = x + 30. What is x?
3. 3.Solve: 6(t − 1) = 4t + 10. What is t?
4. 4.A father is 54 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?
5. 5.Solve: 5(t − 2) = 2t + 35. What is t?
6. 6.Solve: 4n + 13 = 2n + 15. What is n?
7. 7.Solve: 7t + 11 = 6t + 24. What is t?
8. 8.Solve: x/3 + x/5 = 56. What is x?
9. 9.Solve: 6(t − 4) = 4t + 12. What is t?
10. 10.Solve: 3(m − 5) = m + 5. What is m?
11. 11.Solve: 5(t − 5) = 2t + 32. What is t?
12. 12.The length of a rectangle is 8 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
13. 13.The sum of four consecutive whole numbers is 218. What is the largest of them?
14. 14.Solve: 6(x − 5) = x + 30. What is x?
15. 15.The sum of three consecutive whole numbers is 183. What is the largest of them?
16. 16.A father is 15 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
17. 17.Solve: 7m + 11 = 2m + 31. What is m?
18. 18.The length of a rectangle is 11 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
19. 19.A father is 19 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
20. 20.The length of a rectangle is 6 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
21. 21.The sum of two consecutive whole numbers is 119. What is the largest of them?
22. 22.The sum of three consecutive whole numbers is 156. What is the largest of them?
23. 23.The sum of three consecutive whole numbers is 66. What is the smallest of them?
24. 24.A father is 36 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?
25. 25.Solve: 8x + 4 = 7x + 17. What is x?
26. 26.The length of a rectangle is 5 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
27. 27.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?
28. 28.Solve: 5(y − 2) = 4y + 12. What is y?
29. 29.The sum of two consecutive whole numbers is 59. What is the smallest of them?
30. 30.The sum of four consecutive whole numbers is 238. What is the smallest of them?
31. 31.A father is 15 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
32. 32.Solve: 3(x − 1) = x + 3. What is x?
33. 33.A father is 11 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
34. 34.Solve: t/5 + t/6 = 22. What is t?
35. 35.Solve: t/2 + t/6 = 12. What is t?
36. 36.The sum of two consecutive whole numbers is 85. What is the smallest of them?
37. 37.The length of a rectangle is 14 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
38. 38.Solve: 6(p − 2) = 2p + 4. What is p?
39. 39.Solve: 4t + 4 = 2t + 16. What is t?
40. 40.Solve: p/2 + p/4 = 21. What is p?

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