Chapter 5: Algebra... Different "Faces" of Algebra (I)

The total length of 4 roads is (3x - 1) km. What are the possible lengths of the 4 roads in kilometres?

e.g. The length of the 4 roads are: x km, x km, x-7 km, 6 km
Check: x + x + (x - 7) + 6 = 3x - 1

1. 1/2x, 1/2x, 1/2x, 1.5x - 1

2. 3x-4,1,1,1
(3x-4)+1+1+1

3. x-1, 3/4x, 1/4x, x

4. Another possible lengths are, x km, x/2 km, x/2 km, x-1 km

5. The length of the 4 roads are: 5km, 5km, 4km and 3km, saying that x=6km

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7. The length of the 4 roads are: x km, x km, x-8 km, 7 km
Check: x + x + (x - 8) + 7 = 3x - 1

8. The length of the 4 roads are x km, x+9km , x-10km, x km

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11. The length of the 4 roads are 1 1/2x-1 , 1/2x ,1/2x ,1/2x

12. x-6, x+1,1/2x + 1 1/2, 1/2x + 2 1/2

13. 1/2x-1 + 1/2x +x + x

14. (3x-1)/4 , (3x-1)/4, (3x-1)/4, (3x-1)/4

15. [x+x+(x-100000000000000000000)+99999999999999999999]km

16. 1/2x, 1/2x, x + 1, 1.5x

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18. 1/2x, 1/2x, x - 1, 1.5x

19. x, x-1, 1/2x and 1/2x

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21. 1x, 1x, 0.9x

22. 1/4x + 3/4x + 3x + x-1

23. 1/2x, 1/2x, x - 1, 2.5x

24. 1/3x + 2/3x + x-0.5 + 2x

25. x+x+(-x+1)+x

26. x, x-1, 1/2x, 1/2x

27. 2x+1/2x+1/2x+x-1

28. x, x, x-2, 1

29. 2x, 3/8x, 5/8x, 1/8x-(8-1), 6