Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 84 · 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(y − 4) = 5y + 4. What is y?
2. 2.The length of a rectangle is 3 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
3. 3.The length of a rectangle is 9 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
4. 4.Solve: 3n + 15 = 2n + 25. What is n?
5. 5.The sum of three consecutive whole numbers is 63. What is the smallest of them?
6. 6.Solve: 9p + 4 = 3p + 76. What is p?
7. 7.Solve: 6x + 13 = 2x + 37. What is x?
8. 8.The sum of four consecutive whole numbers is 150. What is the largest of them?
9. 9.The sum of four consecutive whole numbers is 218. What is the smallest of them?
10. 10.Solve: y/4 + y/6 = 25. What is y?
11. 11.Solve: m/3 + m/4 = 28. What is m?
12. 12.A father is 30 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?
13. 13.Solve: 3(x − 5) = 2x + 8. What is x?
14. 14.The length of a rectangle is 12 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
16. 16.The length of a rectangle is 9 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
17. 17.The sum of four consecutive whole numbers is 118. What is the largest of them?
18. 18.Solve: x/2 + x/4 = 18. What is x?
19. 19.Solve: p/2 + p/3 = 5. What is p?
20. 20.Solve: 6(x − 1) = 2x + 42. What is x?
21. 21.Solve: 5(m − 1) = m + 47. What is m?
22. 22.Solve: 7p + 13 = p + 43. What is p?
23. 23.Solve: t/2 + t/6 = 32. What is t?
24. 24.Solve: 8p + 16 = 2p + 58. What is p?
25. 25.The length of a rectangle is 6 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
26. 26.Solve: 3(y − 2) = 2y + 10. What is y?
27. 27.The length of a rectangle is 4 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
28. 28.Solve: y/3 + y/5 = 48. What is y?
29. 29.The sum of four consecutive whole numbers is 122. What is the largest of them?
30. 30.A father is 12 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?
31. 31.A father is 45 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
32. 32.Solve: x/6 + x/4 = 15. What is x?
33. 33.The sum of two consecutive whole numbers is 17. What is the smallest of them?
34. 34.Solve: 4(p − 2) = p + 1. What is p?
35. 35.Solve: y/4 + y/3 = 7. What is y?
36. 36.The length of a rectangle is 2 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
37. 37.The length of a rectangle is 13 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
38. 38.A father is 11 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
39. 39.A father is 33 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?
40. 40.The length of a rectangle is 4 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?

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