Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 730 · 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: 8m + 17 = 7m + 23. What is m?
2. 2.Solve: 5p + 19 = 4p + 27. What is p?
3. 3.Solve: 3(x − 1) = 2x + 5. What is x?
4. 4.Solve: 6(p − 1) = 2p + 18. What is p?
5. 5.The sum of two consecutive whole numbers is 99. What is the smallest of them?
6. 6.The length of a rectangle is 1 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
7. 7.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
8. 8.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
9. 9.A father is 32 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?
10. 10.Solve: 5(p − 1) = p + 15. What is p?
11. 11.A father is 15 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?
12. 12.The length of a rectangle is 12 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
13. 13.The sum of two consecutive whole numbers is 29. What is the largest of them?
14. 14.The sum of two consecutive whole numbers is 75. What is the smallest of them?
15. 15.Solve: x/6 + x/5 = 77. What is x?
16. 16.Solve: 5(m − 4) = m + 20. What is m?
17. 17.The length of a rectangle is 3 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
18. 18.Solve: t/6 + t/3 = 24. What is t?
19. 19.The sum of three consecutive whole numbers is 75. What is the smallest of them?
20. 20.Solve: t/5 + t/6 = 44. What is t?
21. 21.Solve: 5(m − 1) = 3m + 15. What is m?
22. 22.A father is 33 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
23. 23.Solve: 5(t − 1) = 2t + 28. What is t?
24. 24.Solve: 6t + 19 = 3t + 34. What is t?
25. 25.Solve: 4(x − 4) = x + 35. What is x?
26. 26.A father is 16 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.The sum of four consecutive whole numbers is 70. What is the smallest of them?
28. 28.Solve: y/3 + y/4 = 49. What is y?
29. 29.Solve: 4(p − 5) = 2p + 18. What is p?
30. 30.Solve: 4t + 16 = t + 22. What is t?
31. 31.Solve: 6n + 7 = n + 22. What is n?
32. 32.Solve: x/6 + x/4 = 15. What is x?
33. 33.The sum of two consecutive whole numbers is 107. What is the largest of them?
34. 34.Solve: 6y + 3 = 4y + 17. What is y?
35. 35.Solve: n/5 + n/2 = 28. What is n?
36. 36.The length of a rectangle is 2 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
37. 37.The length of a rectangle is 10 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
38. 38.The length of a rectangle is 13 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
39. 39.Solve: y/3 + y/6 = 15. What is y?
40. 40.A father is 13 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?

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