Question 844280: Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x-2 and the largest odd number less than 3x+5 can be written in the form ax+b. What is a + B?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x is an even integer.
you are looking for the positive difference between the following:
smallest odd number greater than 7x-2
greatest odd number less than 3x+5
if x is an even number that is positive, then the positive difference will be the larger number minus the smaller number.
if x is even, then 7x-2 will always be even, so the smallest odd number greater than that will be 1 greater which will be 7x-1.
if x is even, then 3x+5 will always be odd, so the greatest number smaller than that will be 2 less which will be 3x+3.
the positive difference will be (7x-1) - (3x+3) which will be equal to 7x - 1 - 3x - 3 which will be equal to 4x - 4.
this is in the form of ax + b, where a is equal to 4 and b is equal to -4.
the equation is 4x-4.
the following table shows that this formula give you the positive difference each time.
the fourth and fifth column should be the same and they are, confirming this is true.
x 7x-1 3x+3 (7x-1)-(3x+3) (4x-4)
2 13 9 4 4
4 27 15 12 12
6 41 21 20 20
8 55 27 28 28
10 69 33 36 36
12 83 39 44 44
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