Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 759 · 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 sum of three consecutive whole numbers is 78. What is the smallest of them?
2. 2.Solve: 5(y − 1) = 2y + 4. What is y?
3. 3.Solve: 8p + 2 = 5p + 26. What is p?
4. 4.Solve: 4(y − 4) = 2y + 20. What is y?
5. 5.The length of a rectangle is 5 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
6. 6.Solve: 6(y − 2) = y + 48. What is y?
7. 7.The sum of three consecutive whole numbers is 30. What is the largest of them?
8. 8.The sum of four consecutive whole numbers is 74. What is the smallest of them?
9. 9.Solve: 5(p − 5) = 3p + 21. What is p?
10. 10.Solve: n/3 + n/5 = 56. What is n?
11. 11.The length of a rectangle is 14 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
12. 12.The length of a rectangle is 7 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
13. 13.Solve: y/6 + y/2 = 28. What is y?
14. 14.A father is 48 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?
15. 15.Solve: y/3 + y/5 = 40. What is y?
16. 16.Solve: x/4 + x/2 = 15. What is x?
17. 17.The length of a rectangle is 10 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
18. 18.The sum of two consecutive whole numbers is 67. What is the smallest of them?
19. 19.The sum of three consecutive whole numbers is 48. What is the smallest of them?
20. 20.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?
21. 21.Solve: 6(p − 1) = 3p + 21. What is p?
22. 22.A father is 27 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?
23. 23.Solve: m/6 + m/4 = 30. What is m?
24. 24.The length of a rectangle is 2 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
25. 25.The length of a rectangle is 15 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
26. 26.A father is 14 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?
27. 27.Solve: 3(p − 4) = 2p + 7. What is p?
28. 28.The length of a rectangle is 14 cm more than its width. Its perimeter is 148 cm. What is its width (in cm)?
29. 29.The length of a rectangle is 9 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
30. 30.Solve: 5(x − 1) = 3x + 5. What is x?
31. 31.Solve: 7x + 20 = 6x + 23. What is x?
32. 32.Solve: 3t + 19 = 2t + 29. What is t?
33. 33.Solve: n/5 + n/3 = 32. What is n?
34. 34.The length of a rectangle is 6 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
35. 35.Solve: 4(m − 1) = 2m + 2. What is m?
36. 36.A father is 9 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
37. 37.Solve: m/3 + m/5 = 48. What is m?
38. 38.Solve: 3x + 5 = x + 29. What is x?
39. 39.Solve: 9x + 6 = 2x + 20. What is x?
40. 40.Solve: 6(n − 4) = 3n + 18. What is n?

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