Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 614 · 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(t − 3) = 2t + 10. What is t?
2. 2.A father is 27 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?
3. 3.Solve: 6(p − 3) = 3p + 30. What is p?
4. 4.The sum of four consecutive whole numbers is 158. What is the smallest of them?
5. 5.Solve: 6(y − 2) = 5y + 7. What is y?
6. 6.The length of a rectangle is 13 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
7. 7.Solve: 4(t − 3) = 3t + 6. What is t?
8. 8.A father is 28 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?
9. 9.Solve: 6(t − 2) = t + 23. What is t?
10. 10.Solve: 6(t − 3) = 5t + 13. What is t?
11. 11.The length of a rectangle is 3 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
12. 12.Solve: 4y + 3 = 2y + 19. What is y?
13. 13.A father is 36 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?
14. 14.A father is 16 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?
15. 15.The sum of two consecutive whole numbers is 27. What is the largest of them?
16. 16.Solve: m/4 + m/2 = 24. What is m?
17. 17.The length of a rectangle is 2 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
18. 18.A father is 38 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
19. 19.Solve: 5(n − 2) = n + 2. What is n?
20. 20.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
21. 21.Solve: 4(n − 5) = 2n + 20. What is n?
22. 22.Solve: 9p + 19 = 5p + 23. What is p?
23. 23.A father is 10 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: 5(n − 3) = n + 17. What is n?
25. 25.The length of a rectangle is 4 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
26. 26.Solve: 5p + 20 = p + 40. What is p?
27. 27.Solve: 6(y − 3) = y + 37. What is y?
28. 28.The length of a rectangle is 12 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
29. 29.The length of a rectangle is 11 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
30. 30.Solve: 9p + 8 = 6p + 41. What is p?
31. 31.Solve: 3(y − 4) = 2y + 9. What is y?
32. 32.Solve: 4t + 19 = 2t + 25. What is t?
33. 33.Solve: 3(t − 5) = t + 23. What is t?
34. 34.A father is 48 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?
35. 35.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?
36. 36.Solve: 6m + 2 = 4m + 14. What is m?
37. 37.Solve: 5(t − 3) = t + 45. What is t?
38. 38.Solve: 6x + 16 = 4x + 36. What is x?
39. 39.A father is 36 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?
40. 40.Solve: p/5 + p/3 = 56. What is p?

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