### Chapter 5: Algebra... Different "Faces" of Algebra (II)

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. 2x+x/2+(x/2+5)+1=3x-1 :)

1. Checking: 2x+x/2+(x/2-5)+4=3x-1
Lengths: 2x, x/2, (x/2-5), 4

2. Did it wrongly, sry.....

3. Firstly, x is a natural number, rational number and is a integer.
My x must be greater than 0 (No negative)

4. x can be 1-∞

5. Revised: x∈Z R N

2. The length of the 4 roads are: 1/2x, 1/2x, x, x-1....
Check: 1/2x + 1/2x + x + (x-1) = 3x-1

1. Conditions: The lengths must be positive integers.

3. The length of the 4 roads are: x-10 km, x+4 km, x km, 5 km
Check: (x-10) , (x+4) , x , 5 = 3x - 1

1. Conditions: x must be 10>

4. The lengths are: (x) km, (0.75x) km, (0.25x) km, (x-1) km

Check: x + 0.75x + 0.25x + (x-1) = (3x-1) km

1. The conditions are: It cannot be 1 and below
Check: (x-1) * If x is 1*
(x-1) = 0 km * That is not possible for a road to be 0 km*

Check: (x-1) * If x is 1.1*
(x-1) = 0.1 km * That is possible for a road to be 0.1 km*

5. The possible lengths is (3x-1)/4 km for each of the road.

1. Check: (3x-1)/4 + (3x-1)/4 + (3x-1)/4 + (3x-1)/4 = (3x - 1) km

2. The possible lengths are 1 km, x+3 km,x+6 km, x-11 km.
Check: (1+x+3+x+6+x-11) km = (3x-1) km

Conditions:
X cannot be 0, cannot be less than 11.

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7. (3x-1)/4km * 4 = 3x-1km

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9. x km +x km +x-10 km+9 km
Check: x km +x km +x-10 km+9 km=(3x - 1) km.

1. The lengths are x km, x km x-10 km and 9km

2. My x is greater than 10.

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11. (3x-1)/4km for each road. Since there are four roads, and each of the roads is (3x-1)/4, then the total of the four roads is obviously 3x-1km when you add them up together. Thank you you

1. The lengths of the roads are: 1 1/4 x km, x-1 km, 2/4 x km, 1/4 x km.
Let's check with Chun Leong! 1 1/4 x + x-1 +2/4 x, 1/4 x km.
YAY!

12. Ans : (3x-1)/4km.
check:(3x-1)/4km+(3x-1)/4km+(3x-1)/4km+(3x-1)/4km=(3x-1)km

1. For (3x-1)/4, x must be 1 or larger.

13. The length of the 4 roads are: (2x-x)km,(3x-2x)km,(7x-6x)km,(7-7+1)km
Check: (2x-x)km + (3x-2x) + (7x - 6x) + (7-7-1)= 3x - 1

14. x, x-2,x-10,11
Check:x+(x-2)+(x-10)+11=3x-1

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16. The possible lengths of the 4 roads are: 1/2x, 1/2x, x, x-1....
Check: 1/2x + 1/2x + x + (x-1) = 3x-1

1. this is true if the variable is a positive integer
XD

17. x km+ x km,+x-7 km,+6 km=3x-1

1. the possible lengths of the 4roads x,x,x+7,6

18. The length of the 4 roads are: (x-1) km, (0.8x) km, (0.2x) km, x km
Check: (x-1) + (0.8x) + (0.2x) + x = 3x - 1

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19. (4x - 3x +1 ) km + (7x - 6x -1) km+ (99 x -98x)km + -1km

CHECK:(4x - 3x +1 ) km + (7x - 6x -1) km+ (99 x -98x)km + -1km = 3x-1

20. Possible lengths of the 4 roads : 2 km, x-6 km, x+14 km, x-11km
Check : (2+x-6+x+14+x-11)km = (3x-1)km

These roads are of different lengths and they are measureable, they are not intergers but in decimal places.
They all also add up to be 3x-1

1. my x is greater than 1

22. x km,x km,x-20km,19km
This would only work if x is greater than 20km

23. (x-1)km,(x-2)km,(x-3)km,5km

24. The possible length of the four roads can be x km, x+15km, x-17km, 1 km

Check: X km+x+15 km+x-17 km+1 km=3x -1

x has to be greater than one for the lengths of the roads to be possible.

25. The possible length are: x km + (x-5)km + (x-2)km + 6km
Check : x km + (x-5)km + (x-2)km + 6km= 3x-1

1. It will only work when x is greater than 5km

26. The possible lengths of the 4 roads are:x+2,x-2,x/2,x/2-1.
Check:x+2+x-2+x/2+x/2-1=3x-1