for how many integers x is the value of -6/(x+1) an integer?

Answer 1

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.

Answer 2

-6/(x+1) is an integer for any factor of 6. let x+1 = {all integer factors of 6 (+/-)}; finding x follows trivially.

Answer 3

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

Answer 4

*now

Answer 5

nvr mind i just figured it out. its eight. thanks!