Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 399 · 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(y − 2) = 3y + 1. What is y?
2. 2.A father is 22 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?
3. 3.The length of a rectangle is 2 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
4. 4.Solve: x/4 + x/3 = 7. What is x?
5. 5.The sum of three consecutive whole numbers is 18. What is the smallest of them?
6. 6.Solve: m/2 + m/3 = 35. What is m?
7. 7.Solve: 3y + 19 = 2y + 32. What is y?
8. 8.Solve: 4(m − 4) = 2m + 2. What is m?
9. 9.Solve: 5t + 11 = 4t + 14. What is t?
10. 10.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?
11. 11.Solve: n/2 + n/3 = 5. What is n?
12. 12.Solve: 6(m − 1) = 3m + 6. What is m?
13. 13.A father is 12 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?
14. 14.The sum of two consecutive whole numbers is 37. What is the largest of them?
15. 15.A father is 20 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?
16. 16.The sum of three consecutive whole numbers is 165. What is the largest of them?
17. 17.Solve: y/4 + y/3 = 21. What is y?
18. 18.Solve: 3(p − 4) = p + 10. What is p?
19. 19.The sum of three consecutive whole numbers is 90. What is the smallest of them?
20. 20.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?
21. 21.Solve: 5p + 15 = 3p + 17. What is p?
22. 22.Solve: 4y + 10 = 2y + 18. What is y?
23. 23.Solve: 5(n − 3) = 3n + 17. What is n?
24. 24.Solve: 5(p − 1) = p + 47. What is p?
25. 25.Solve: p/4 + p/5 = 27. What is p?
26. 26.Solve: 6y + 11 = 4y + 29. What is y?
27. 27.Solve: 9n + 7 = n + 39. What is n?
28. 28.Solve: 4(y − 3) = 2y + 2. What is y?
29. 29.The length of a rectangle is 3 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
30. 30.Solve: y/3 + y/5 = 8. What is y?
31. 31.The sum of three consecutive whole numbers is 180. What is the largest of them?
32. 32.The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
33. 33.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
34. 34.A father is 9 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
35. 35.The length of a rectangle is 13 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
36. 36.The length of a rectangle is 12 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
37. 37.A father is 7 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
38. 38.Solve: 3n + 3 = n + 27. What is n?
39. 39.The length of a rectangle is 2 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
40. 40.Solve: t/6 + t/2 = 16. What is t?

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