Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 702 · 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: 4(y − 4) = 2y + 12. What is y?
2. 2.Solve: 5(x − 1) = x + 23. What is x?
3. 3.Solve: 4m + 6 = 3m + 20. What is m?
4. 4.A father is 6 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
5. 5.The length of a rectangle is 5 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
6. 6.The sum of two consecutive whole numbers is 31. What is the smallest of them?
7. 7.The sum of three consecutive whole numbers is 108. What is the smallest of them?
8. 8.The sum of four consecutive whole numbers is 86. What is the largest of them?
9. 9.Solve: 4x + 14 = 2x + 30. What is x?
10. 10.Solve: 3(t − 4) = t + 26. What is t?
11. 11.Solve: 5x + 7 = x + 19. What is x?
12. 12.The length of a rectangle is 10 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
13. 13.A father is 42 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?
14. 14.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?
15. 15.Solve: x/4 + x/3 = 14. What is x?
16. 16.Solve: 5p + 1 = 4p + 4. What is p?
17. 17.Solve: p/2 + p/4 = 9. What is p?
18. 18.Solve: y/4 + y/2 = 3. What is y?
19. 19.Solve: 6y + 8 = 4y + 32. What is y?
20. 20.The sum of three consecutive whole numbers is 162. What is the largest of them?
21. 21.Solve: y/2 + y/6 = 32. What is y?
22. 22.The length of a rectangle is 10 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
23. 23.Solve: 5m + 5 = m + 61. What is m?
24. 24.The length of a rectangle is 1 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
25. 25.The length of a rectangle is 9 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
26. 26.Solve: 6(y − 3) = 3y + 21. What is y?
27. 27.The sum of four consecutive whole numbers is 166. What is the smallest of them?
28. 28.The length of a rectangle is 10 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
29. 29.Solve: 8p + 4 = 6p + 6. What is p?
30. 30.Solve: 9t + 18 = t + 74. What is t?
31. 31.The sum of four consecutive whole numbers is 230. What is the largest of them?
32. 32.The sum of two consecutive whole numbers is 35. What is the smallest of them?
33. 33.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
34. 34.Solve: 3(n − 5) = 2n + 3. What is n?
35. 35.A father is 30 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
36. 36.A father is 16 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?
37. 37.Solve: 8m + 3 = 3m + 63. What is m?
38. 38.Solve: 3(x − 1) = 2x + 2. What is x?
39. 39.Solve: t/6 + t/2 = 8. What is t?
40. 40.The sum of three consecutive whole numbers is 60. What is the largest of them?

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