for how many integers x is the value of -6/(x+1) an integer?
Well, x+1=6/n where n is an integer.
x= 6/n - 1
so if the left hand sides is an integer, the right hand side is also.
as I see it, the right side will be an integer if 6/n is an integer.
That happens if n=1,2,3,6 or -1,-2,-3,-6
so lets try those:
x= 6/n-1
n...x
-6..-7
-3..-2
and you can do the rest. But I think if if there are only 8 values of n, there are only 8 values of x. See if that is so.
-6/(x+1) is an integer for any factor of 6. let x+1 = {all integer factors of 6 (+/-)}; finding x follows trivially.
sigh...sorry I'm so lost...we are not actually going over this know in school, this is just a practice problem, so yeah if you could please explain again? thnaks
*now
nvr mind i just figured it out. its eight. thanks!
To determine the number of integers for which the value of -6/(x+1) is also an integer, we need to first understand the conditions under which the division of two integers results in an integer.
For the division of two integers to yield an integer, the numerator (-6 in this case) must be divisible evenly by the denominator (x+1). In other words, -6 must be a multiple of (x+1).
So, we need to find the factors or divisors of -6 and determine which ones are of the form (x+1). Let's list the divisors of -6:
-6 divided by 1 equals -6
-6 divided by 2 equals -3
-6 divided by 3 equals -2
-6 divided by 6 equals -1
By comparing these divisors with the possible values of x+1, we can determine which integers satisfy the condition.
For x+1 = 1, -6 is not a multiple.
For x+1 = 2, -6 is not a multiple.
For x+1 = 3, -6 is a multiple.
For x+1 = 6, -6 is not a multiple.
Therefore, we see that the values of x for which -6/(x+1) is an integer are x = 2 and x = 5. Hence, the answer is two integers, specifically x = 2 and x = 5.