Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 763 · 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: 3(n − 2) = 2n + 5. What is n?
2. 2.Solve: 8y + 13 = 5y + 31. What is y?
3. 3.Solve: 4(n − 3) = n + 15. What is n?
4. 4.A father is 22 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
5. 5.The length of a rectangle is 6 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
6. 6.Solve: n/5 + n/2 = 21. What is n?
7. 7.The sum of four consecutive whole numbers is 78. What is the largest of them?
8. 8.Solve: 6t + 9 = 2t + 21. What is t?
9. 9.Solve: 3(m − 5) = m + 19. What is m?
10. 10.The sum of two consecutive whole numbers is 113. What is the largest of them?
11. 11.The length of a rectangle is 13 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
12. 12.A father is 9 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
13. 13.The sum of three consecutive whole numbers is 105. What is the smallest of them?
14. 14.Solve: 4(y − 4) = y + 26. What is y?
15. 15.The length of a rectangle is 1 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
16. 16.A father is 5 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
17. 17.The sum of four consecutive whole numbers is 66. What is the largest of them?
18. 18.The sum of three consecutive whole numbers is 159. What is the largest of them?
19. 19.Solve: 3m + 10 = m + 14. What is m?
20. 20.Solve: 7p + 6 = 6p + 11. What is p?
21. 21.Solve: 5(y − 2) = 3y + 10. What is y?
22. 22.Solve: 6(t − 4) = 3t + 24. What is t?
23. 23.A father is 11 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
24. 24.Solve: 6m + 16 = 3m + 22. What is m?
25. 25.Solve: 4(m − 5) = m + 1. What is m?
26. 26.Solve: 8p + 3 = 2p + 45. What is p?
27. 27.The sum of four consecutive whole numbers is 118. What is the smallest of them?
28. 28.A father is 12 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
29. 29.The length of a rectangle is 8 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
30. 30.The length of a rectangle is 10 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
31. 31.Solve: 5t + 13 = 2t + 52. What is t?
32. 32.The length of a rectangle is 15 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
33. 33.Solve: 9y + 4 = 5y + 24. What is y?
34. 34.Solve: t/4 + t/2 = 3. What is t?
35. 35.Solve: y/6 + y/4 = 20. What is y?
36. 36.A father is 18 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?
37. 37.Solve: p/3 + p/2 = 15. What is p?
38. 38.Solve: 6(t − 3) = 3t + 6. What is t?
39. 39.A father is 21 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?
40. 40.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?

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