The next smallest integer would be 2 less, so
7y+9 - 2
= .....
hint: take out a common factor and it will be obvious
a. 7(y-2)+1
b. 7(y-2)
c. 7(y+3)
d. 7(y+2)
e. 7(y+1)
7y+9 - 2
= .....
hint: take out a common factor and it will be obvious
The correct option to represent the next smallest odd integer is:
a. 7(y-2)+1
So the answer is a. 7(y-2)+1.
Given that 7y + 9 represents an odd integer, we can start by simplifying it.
We know that 7y will always be divisible by 7 because it is being multiplied by 7. So, if we divide 7 by 7, we get 1.
Since 7y/7 = y, we can rewrite the expression as y + 9.
Now, we need to find the next smallest odd integer. To do that, we can subtract 2 from y.
The options given are:
a. 7(y-2) + 1
b. 7(y-2)
c. 7(y+3)
d. 7(y+2)
e. 7(y+1)
If we substitute y with y-2 in each option, we'll be able to determine which one results in an odd integer.
a. 7((y-2)-2) + 1 = 7(y-4) + 1
b. 7((y-2)) = 7(y-2)
c. 7((y+2)) = 7(y+3)
d. 7((y+2)+2) = 7(y+4)
e. 7((y+2)+1) = 7(y+3)
Since the question asks for the next smallest odd integer, we can eliminate options (c), (d), and (e) since they result in larger values than the original expression 7y + 9.
We are left with options (a) and (b):
a. 7(y-4) + 1
b. 7(y-2)
In order for the expression to be an odd integer, the coefficient of y (in this case, 7) must remain the same. So, option (a) changes the coefficient to 7(y-4), making it different from the original expression 7y + 9.
Therefore, the correct answer is option (b), 7(y-2), which represents the next smallest odd integer.