Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 942 · 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: t/2 + t/6 = 4. What is t?
2. 2.A father is 22 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
3. 3.Solve: 6x + 18 = 3x + 57. What is x?
4. 4.The sum of two consecutive whole numbers is 53. What is the largest of them?
5. 5.Solve: 9n + 14 = 3n + 104. What is n?
6. 6.Solve: t/2 + t/3 = 10. What is t?
7. 7.Solve: y/5 + y/2 = 28. What is y?
8. 8.A father is 14 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
9. 9.Solve: n/2 + n/6 = 8. What is n?
10. 10.Solve: 5(x − 2) = x + 22. What is x?
11. 11.Solve: p/6 + p/5 = 77. What is p?
12. 12.The length of a rectangle is 14 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
13. 13.A father is 21 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?
14. 14.The length of a rectangle is 2 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
15. 15.The length of a rectangle is 12 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
16. 16.Solve: 9p + 18 = 5p + 50. What is p?
17. 17.Solve: 4(p − 5) = 3p + 2. What is p?
18. 18.Solve: 5(y − 4) = 3y + 24. What is y?
19. 19.The length of a rectangle is 1 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
20. 20.A father is 42 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?
21. 21.Solve: y/3 + y/4 = 56. What is y?
22. 22.The length of a rectangle is 9 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
23. 23.Solve: 3x + 15 = x + 25. What is x?
24. 24.Solve: 4(y − 4) = y + 2. What is y?
25. 25.Solve: 3x + 17 = x + 45. What is x?
26. 26.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
27. 27.A father is 16 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?
28. 28.Solve: m/5 + m/6 = 66. What is m?
29. 29.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
30. 30.Solve: 4(t − 4) = t + 29. What is t?
31. 31.Solve: n/3 + n/4 = 28. What is n?
32. 32.Solve: 5(y − 1) = 2y + 34. What is y?
33. 33.The sum of four consecutive whole numbers is 222. What is the smallest of them?
34. 34.A father is 18 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?
35. 35.The sum of two consecutive whole numbers is 13. What is the smallest of them?
36. 36.The sum of two consecutive whole numbers is 113. What is the largest of them?
37. 37.A father is 6 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
38. 38.A father is 7 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
39. 39.The length of a rectangle is 6 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
40. 40.A father is 20 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?

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