Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 446 · 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: 4(m − 4) = m + 8. What is m?
2. 2.A father is 54 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?
3. 3.Solve: 4(y − 2) = 2y + 6. What is y?
4. 4.Solve: 4(y − 3) = y + 21. What is y?
5. 5.The length of a rectangle is 2 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
6. 6.The length of a rectangle is 5 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
7. 7.The sum of three consecutive whole numbers is 69. What is the smallest of them?
8. 8.Solve: 4t + 19 = 2t + 31. What is t?
9. 9.Solve: 9t + 20 = 3t + 44. What is t?
10. 10.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
11. 11.A father is 30 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?
12. 12.Solve: t/6 + t/2 = 4. What is t?
13. 13.Solve: 6(t − 3) = 2t + 30. What is t?
14. 14.Solve: 4m + 13 = 2m + 33. What is m?
15. 15.The length of a rectangle is 6 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
16. 16.Solve: 4(p − 4) = p + 35. What is p?
17. 17.Solve: 4(x − 2) = x + 31. What is x?
18. 18.A father is 42 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?
19. 19.The length of a rectangle is 11 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
20. 20.Solve: 6m + 14 = 3m + 23. What is m?
21. 21.Solve: 3(p − 1) = p + 21. What is p?
22. 22.Solve: 5(m − 4) = 2m + 16. What is m?
23. 23.The length of a rectangle is 7 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
24. 24.The length of a rectangle is 8 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
25. 25.Solve: y/3 + y/6 = 12. What is y?
26. 26.The sum of two consecutive whole numbers is 49. What is the largest of them?
27. 27.The length of a rectangle is 4 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
28. 28.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
29. 29.Solve: 3(y − 2) = y + 6. What is y?
30. 30.Solve: m/6 + m/3 = 15. What is m?
31. 31.The sum of three consecutive whole numbers is 171. What is the smallest of them?
32. 32.Solve: 6(x − 2) = 2x + 8. What is x?
33. 33.Solve: x/5 + x/2 = 42. What is x?
34. 34.Solve: 4(y − 1) = 3y + 6. What is y?
35. 35.Solve: 6(y − 1) = y + 9. What is y?
36. 36.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
37. 37.The sum of three consecutive whole numbers is 165. What is the smallest of them?
38. 38.The length of a rectangle is 13 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
39. 39.Solve: 4x + 16 = x + 43. What is x?
40. 40.A father is 24 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?

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