### 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

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The following are correct...
• 2x, x, x + 2, 1- x
• 0.5x , x, x, 0.5x - 1
• 0.25x, 0.75x, 1.25x, 0.75x-1
• x, x, x-8, 7
• 0.25x , 0.75x, 1, x-2
• 0.75x, 0.25x - 1, 1.5x, 0.5x
• x-1, x, 4/6 x, 2/6 x
In class (21 April),  we discussed that these lengths are only valid if "x" satisfies some condition.
e.g 1: In the example of lengths, x, x, x-8 and 7
values of x must be greater than 8, otherwise x-8 would not be valid (in this context)
e.g. 2: In the example of lengths, 0.25x, 0.75x, 1 and x-2
values of x must be at greater than 2, otherwise x-2 would not be valid (in this context)
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What's wrong with the following?
• 2x-1, 0.5x, 0.25x, 0.25
• 0.5x, 0.5x, 0.5x-1, 1.5x
•  xx, x, (-1)
• 2x, 0.5x, 0.5x, -1
• 8, 4x, -x, -7
In class (21 April), we discussed where goes wrong with this lengths:
• The sum might not have added up to the given expression, 3x - 1
• The context (as length of road is a positive number)

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

-Ishani♛♠⚑♪

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3. The possible length of the 4 roads are:
2x km,1x km,1x km + 2km,1km-1x km

4. Check:2x km+1x km+1x km-1x km+2km-1km=(3x+1)km

5. 1/2 x , 1x, 1x, 1/2x - 1

Check : 1/2x km + 1x km + 1x km + 1/2 x km -1 km = 3x-1km

6. ((7x-1x)/2)-1

Check: 7x-1x=6x
6x/2=3x
3x-1=(3x-1)

7. 0.25x km,0.75x km,1.25x km,0.75x-1 km

Check:0.25x km+0.75x km+1.25x km+(0.75x-1) km=(3x-1) km

8. xkm+xkm+x-8km+7km
x + x + (x - 8) + 7 = 3x - 1

9. 2x,0.5x,0.5x,-1km
Check : 2x+0.5x+0.5x = 3x
3x+-1km = (3x-1)km

10. 1/2 x , 1x, 1x, 1/2x - 1 (All are in Km)

Check:1/2x km + 1x km + 1x km + 1/2 x km -1 km = 3x-1km

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12. (3/4x)km, (1/4x-1)km, (1 1/2x)km, (1/2x)km

Check: (3/4x)km+(1/4x-1)km+(1 1/2x)km+(1/2x)km=(3x-1)km

13. 1/2 X km,1/2 X km,1/2 X -1km,1 1/2 X km

Check:1/2X km+1/2 X km+(1/2 X -1)km+1 1/2 X km=(3x-1)km

14. (3x - 1) km

The length of the 4 roads are: 8 km, 4x km, (-x) km, (-7)km

Check: 8+4x+(-x)+(-7)= 3x-1

15. X km-1km, X km, 4/6 X km, 2/6 X km

Check: (X km-1km)+X km+4/6 X km+2/6 X k= (3x-1)km

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17. 2x km- 1 km, 1/2x km, 1/4x km, 1/4 km

Check: (2x km-1 km) + 1/2x km +1/4x km + 1/4x km= 3x km-1 km

18. x, 2x-9km, 4km, 4km
Check: x + 2x-9km + 4km + 4km = 3x-1km

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20. The length of the 4 roads are: x km, x - 11 km, x + 9km, 1 km
Check: x + (x-11) + (x+9) + 1 = 3x - 1

21. 1. (x-9)km, 6km, 2km, 2x.
2x+(x-9)km+6km+2km = (3x-1)km

22. (-x)+(2x)+(x+8)+(x-9)

23. Mark :) :( :&#39;( (^^^) :D :O :42: O:) :p 3:)4/21/2011 08:21:00 AM

-x-2x+4x+24+x-25

24. 1/4x , 3/4x, 1, (2x-2)

Check: 1/4x+3/4x+1+(2x-2) = (3-1)km

25. Answer : (x -10)km , x km , (x + 6)km , 3km

Check : x km + ( x- 10)km + ( x + 6)km + 3km= ( 2x-10) + ( x + 6)km+ 3km = ( 3x-4)km+ 3km = (3x-1)km.