Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 651 · 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: 6(t − 4) = 4t + 16. What is t?
2. 2.Solve: 7m + 4 = 3m + 48. What is m?
3. 3.The length of a rectangle is 14 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
4. 4.The sum of three consecutive whole numbers is 123. What is the largest of them?
5. 5.The sum of four consecutive whole numbers is 74. What is the smallest of them?
6. 6.A father is 20 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
7. 7.A father is 42 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?
8. 8.Solve: 4(n − 3) = 2n + 18. What is n?
9. 9.Solve: n/5 + n/4 = 63. What is n?
10. 10.Solve: 3t + 7 = t + 21. What is t?
11. 11.Solve: 4(m − 4) = m + 5. What is m?
12. 12.The sum of three consecutive whole numbers is 159. What is the largest of them?
13. 13.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
14. 14.The sum of three consecutive whole numbers is 105. What is the smallest of them?
15. 15.Solve: 4(p − 2) = p + 37. What is p?
16. 16.Solve: x/3 + x/6 = 3. What is x?
17. 17.The length of a rectangle is 5 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
18. 18.The length of a rectangle is 10 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
19. 19.Solve: 9n + 11 = 6n + 14. What is n?
20. 20.A father is 22 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?
21. 21.The sum of three consecutive whole numbers is 141. What is the largest of them?
22. 22.Solve: n/6 + n/4 = 5. What is n?
23. 23.Solve: y/6 + y/2 = 28. What is y?
24. 24.Solve: 5t + 1 = 3t + 13. What is t?
25. 25.Solve: m/2 + m/3 = 25. What is m?
26. 26.The length of a rectangle is 3 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
27. 27.The length of a rectangle is 7 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
28. 28.Solve: 3(x − 4) = x + 18. What is x?
29. 29.Solve: t/2 + t/4 = 9. What is t?
30. 30.A father is 8 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: t/6 + t/4 = 35. What is t?
32. 32.The length of a rectangle is 10 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
33. 33.Solve: 3y + 15 = 2y + 17. What is y?
34. 34.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
35. 35.The sum of three consecutive whole numbers is 39. What is the smallest of them?
36. 36.Solve: 3(t − 2) = t + 14. What is t?
37. 37.Solve: 6t + 17 = 4t + 43. What is t?
38. 38.Solve: x/3 + x/2 = 10. What is x?
39. 39.A father is 10 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?
40. 40.The sum of three consecutive whole numbers is 180. What is the largest of them?

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