Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 613 · 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: 5(t − 2) = 3t + 8. What is t?
2. 2.Solve: y/2 + y/6 = 20. What is y?
3. 3.A father is 18 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?
4. 4.Solve: 9p + 3 = 5p + 31. What is p?
5. 5.The sum of two consecutive whole numbers is 109. What is the smallest of them?
6. 6.The length of a rectangle is 7 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
7. 7.The sum of three consecutive whole numbers is 138. What is the largest of them?
8. 8.A father is 30 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?
9. 9.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?
10. 10.The length of a rectangle is 13 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
11. 11.Solve: p/5 + p/3 = 24. What is p?
12. 12.The length of a rectangle is 4 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
13. 13.The sum of four consecutive whole numbers is 198. What is the smallest of them?
14. 14.The sum of three consecutive whole numbers is 123. What is the smallest of them?
15. 15.Solve: 8x + 10 = 6x + 38. What is x?
16. 16.The length of a rectangle is 12 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
17. 17.The sum of three consecutive whole numbers is 33. What is the smallest of them?
18. 18.Solve: p/3 + p/4 = 42. What is p?
19. 19.The length of a rectangle is 5 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
20. 20.Solve: 6t + 14 = 4t + 24. What is t?
21. 21.The length of a rectangle is 8 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
22. 22.A father is 18 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
23. 23.A father is 14 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
24. 24.Solve: 4(t − 5) = t + 1. What is t?
25. 25.The sum of two consecutive whole numbers is 35. What is the smallest of them?
26. 26.Solve: 4(m − 1) = 3m + 12. What is m?
27. 27.The length of a rectangle is 5 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
28. 28.Solve: 6p + 16 = p + 51. What is p?
29. 29.Solve: 3(x − 1) = x + 9. What is x?
30. 30.A father is 11 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: 3(p − 3) = p + 9. What is p?
32. 32.A father is 48 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?
33. 33.The length of a rectangle is 6 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
34. 34.Solve: 5m + 13 = 2m + 37. What is m?
35. 35.Solve: y/5 + y/4 = 9. What is y?
36. 36.The sum of four consecutive whole numbers is 62. What is the smallest of them?
37. 37.Solve: p/5 + p/2 = 56. What is p?
38. 38.Solve: 3(x − 1) = x + 1. What is x?
39. 39.Solve: 4(n − 2) = 2n + 26. What is n?
40. 40.The length of a rectangle is 1 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?

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