Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 412 · 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 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
2. 2.Solve: 3(y − 2) = 2y + 7. What is y?
3. 3.The sum of four consecutive whole numbers is 118. What is the smallest of them?
4. 4.Solve: 3n + 11 = n + 13. What is n?
5. 5.Solve: t/6 + t/5 = 88. What is t?
6. 6.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?
7. 7.A father is 9 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
8. 8.The length of a rectangle is 9 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
9. 9.Solve: 6(m − 1) = 5m + 2. What is m?
10. 10.Solve: 5(y − 2) = y + 22. What is y?
11. 11.A father is 10 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
12. 12.The length of a rectangle is 12 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
13. 13.Solve: y/6 + y/2 = 8. What is y?
14. 14.The length of a rectangle is 6 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
15. 15.Solve: 6x + 10 = x + 25. What is x?
16. 16.Solve: 5(x − 5) = 3x + 19. What is x?
17. 17.Solve: n/5 + n/4 = 18. What is n?
18. 18.Solve: 3t + 11 = 2t + 15. What is t?
19. 19.The sum of two consecutive whole numbers is 107. What is the largest of them?
20. 20.Solve: t/2 + t/5 = 49. What is t?
21. 21.Solve: 4(y − 2) = y + 34. What is y?
22. 22.Solve: x/2 + x/6 = 20. What is x?
23. 23.The length of a rectangle is 9 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
24. 24.The length of a rectangle is 6 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
25. 25.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?
26. 26.Solve: 6x + 18 = 2x + 74. What is x?
27. 27.Solve: 9m + 3 = 5m + 55. What is m?
28. 28.A father is 24 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?
29. 29.A father is 14 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?
30. 30.Solve: y/6 + y/3 = 6. What is y?
31. 31.Solve: p/5 + p/2 = 28. What is p?
32. 32.Solve: 7p + 6 = 6p + 10. What is p?
33. 33.Solve: 9x + 6 = 6x + 36. What is x?
34. 34.Solve: 3(y − 1) = 2y + 4. What is y?
35. 35.The sum of three consecutive whole numbers is 123. What is the largest of them?
36. 36.Solve: 3(x − 1) = 2x + 3. What is x?
37. 37.A father is 27 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
38. 38.Solve: x/4 + x/5 = 45. What is x?
39. 39.A father is 39 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?
40. 40.A father is 28 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?

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