Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 982 · 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(x − 1) = 4x + 4. What is x?
2. 2.Solve: 6y + 12 = 5y + 20. What is y?
3. 3.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
4. 4.Solve: 6(t − 2) = 3t + 18. What is t?
5. 5.Solve: 3y + 7 = 2y + 21. What is y?
6. 6.The length of a rectangle is 2 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
7. 7.The length of a rectangle is 8 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
8. 8.Solve: 7t + 10 = 5t + 36. What is t?
9. 9.Solve: y/6 + y/3 = 6. What is y?
10. 10.Solve: 3(y − 2) = y + 4. What is y?
11. 11.The length of a rectangle is 12 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
12. 12.Solve: 3(t − 1) = t + 3. What is t?
13. 13.The length of a rectangle is 3 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
14. 14.Solve: 6(p − 4) = 3p + 27. What is p?
15. 15.Solve: 3y + 12 = 2y + 23. What is y?
16. 16.The sum of two consecutive whole numbers is 99. What is the smallest of them?
17. 17.The sum of four consecutive whole numbers is 42. What is the largest of them?
18. 18.Solve: 5(p − 2) = p + 38. What is p?
19. 19.The sum of four consecutive whole numbers is 66. What is the largest of them?
20. 20.The sum of three consecutive whole numbers is 183. What is the largest of them?
21. 21.A father is 14 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
22. 22.Solve: 3(p − 4) = p + 10. What is p?
23. 23.Solve: 3p + 9 = 2p + 11. What is p?
24. 24.Solve: 6(m − 1) = 2m + 30. What is m?
25. 25.A father is 14 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
26. 26.The length of a rectangle is 13 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
27. 27.Solve: 3(n − 2) = 2n + 6. What is n?
28. 28.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?
29. 29.Solve: 3(y − 5) = y + 3. What is y?
30. 30.A father is 15 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: y/6 + y/3 = 18. What is y?
32. 32.Solve: 8y + 15 = 6y + 41. What is y?
33. 33.The sum of four consecutive whole numbers is 166. What is the smallest of them?
34. 34.The length of a rectangle is 10 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
35. 35.The sum of two consecutive whole numbers is 109. What is the largest of them?
36. 36.A father is 11 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
37. 37.A father is 14 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
38. 38.The sum of two consecutive whole numbers is 113. What is the smallest of them?
39. 39.The length of a rectangle is 2 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
40. 40.The length of a rectangle is 5 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?

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