The number of integers $x$ for which the value of $\frac{-6}{x+1}$ is an integer is
(A) 8
(B) 9
(C) 2
(D) 6
(E) 7
Since $x$ is an integer, then $x+1$ is an integer.

Since $\frac{-6}{x+1}$ is to be integer, then $x+1$ must be a divisor of -6 .

Thus, there are 8 possible values for $x+1$, namely $-6,-3,-2,-1,1,2,3$, and 6 .

This gives 8 possible values for $x$, namely $-7,-4,-3,-2,0,1,2$, and 5 .

ANSWER: (A)