If 7y+9 represents an odd integer, which of the following represents the next smallest odd integer?
a. 7(y-2)+1
b. 7(y-2)
c. 7(y+3)
d. 7(y+2)
e. 7(y+1)
To find the next smallest odd integer, we need to subtract 2 from the given expression, 7y+9.
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.
To determine the next smallest odd integer, we can start by understanding what an odd integer is. An odd integer is any integer that cannot be evenly divided by 2, resulting in a remainder of 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.
The next smallest integer would be 2 less, so
7y+9 - 2
= .....
hint: take out a common factor and it will be obvious