Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 269 · 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 3 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
2. 2.A father is 13 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
3. 3.The sum of two consecutive whole numbers is 15. What is the smallest of them?
4. 4.Solve: 5(n − 3) = n + 17. What is n?
5. 5.Solve: 5(x − 2) = 2x + 35. What is x?
6. 6.Solve: 3n + 17 = 2n + 30. What is n?
7. 7.A father is 51 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?
8. 8.Solve: 4n + 6 = 2n + 14. What is n?
9. 9.Solve: 9y + 7 = 8y + 22. What is y?
10. 10.A father is 12 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?
11. 11.A father is 13 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
12. 12.Solve: x/5 + x/2 = 49. What is x?
13. 13.Solve: y/6 + y/3 = 18. What is y?
14. 14.A father is 27 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?
15. 15.The length of a rectangle is 14 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
16. 16.The sum of three consecutive whole numbers is 147. What is the largest of them?
17. 17.The sum of three consecutive whole numbers is 105. What is the largest of them?
18. 18.Solve: t/4 + t/5 = 45. What is t?
19. 19.The sum of two consecutive whole numbers is 87. What is the smallest of them?
20. 20.The sum of four consecutive whole numbers is 66. What is the largest of them?
21. 21.Solve: y/5 + y/2 = 21. What is y?
22. 22.The length of a rectangle is 14 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
23. 23.Solve: p/5 + p/2 = 49. What is p?
24. 24.Solve: m/6 + m/2 = 8. What is m?
25. 25.Solve: y/2 + y/4 = 3. What is y?
26. 26.The sum of three consecutive whole numbers is 45. What is the smallest of them?
27. 27.Solve: 4m + 2 = 2m + 16. What is m?
28. 28.The length of a rectangle is 9 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
29. 29.Solve: 5m + 12 = 2m + 45. What is m?
30. 30.Solve: 4(p − 4) = p + 23. What is p?
31. 31.The length of a rectangle is 7 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
32. 32.The length of a rectangle is 2 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
33. 33.Solve: 4(m − 2) = 3m + 1. What is m?
34. 34.Solve: m/3 + m/2 = 20. What is m?
35. 35.A father is 8 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?
36. 36.The length of a rectangle is 6 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
37. 37.A father is 18 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?
38. 38.Solve: 4(t − 5) = 3t + 13. What is t?
39. 39.Solve: 7t + 3 = 5t + 33. What is t?
40. 40.Solve: x/3 + x/6 = 3. What is x?

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