Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 184 · 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 2 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
2. 2.A father is 26 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?
3. 3.Solve: 4(p − 3) = p + 30. What is p?
4. 4.Solve: 6(y − 4) = 4y + 2. What is y?
5. 5.A father is 20 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
6. 6.Solve: t/2 + t/3 = 35. What is t?
7. 7.Solve: 5(m − 2) = 2m + 35. What is m?
8. 8.Solve: n/6 + n/4 = 35. What is n?
9. 9.A father is 42 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
10. 10.Solve: 3(p − 1) = p + 19. What is p?
11. 11.The length of a rectangle is 11 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
12. 12.The length of a rectangle is 3 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
13. 13.Solve: 9y + 18 = 7y + 22. What is y?
14. 14.The length of a rectangle is 15 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
15. 15.The sum of four consecutive whole numbers is 162. What is the smallest of them?
16. 16.Solve: y/6 + y/5 = 22. What is y?
17. 17.A father is 39 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
18. 18.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
19. 19.Solve: y/2 + y/3 = 10. What is y?
20. 20.The length of a rectangle is 1 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
21. 21.Solve: y/3 + y/4 = 49. What is y?
22. 22.A father is 24 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?
23. 23.A father is 8 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
24. 24.Solve: 4x + 2 = 3x + 16. What is x?
25. 25.The length of a rectangle is 7 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
26. 26.Solve: x/6 + x/2 = 12. What is x?
27. 27.The length of a rectangle is 9 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
28. 28.The length of a rectangle is 4 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
29. 29.Solve: y/2 + y/4 = 24. What is y?
30. 30.The sum of two consecutive whole numbers is 87. What is the largest of them?
31. 31.Solve: 5x + 6 = 2x + 9. What is x?
32. 32.The sum of two consecutive whole numbers is 109. What is the smallest of them?
33. 33.A father is 33 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?
34. 34.The sum of two consecutive whole numbers is 21. What is the smallest of them?
35. 35.Solve: 7y + 5 = 4y + 14. What is y?
36. 36.Solve: 8m + 7 = 4m + 35. What is m?
37. 37.Solve: 5(x − 1) = x + 15. What is x?
38. 38.Solve: 8y + 11 = 3y + 81. What is y?
39. 39.The sum of four consecutive whole numbers is 194. What is the largest of them?
40. 40.Solve: t/2 + t/3 = 20. What is t?

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