How many integers $x$ satisfy

$$
-5 < x-1 \leq 5 ?
$$

(a) 8
(b) 9
(c) 10
(d) 11
(e) 12
The correct option is (c).

By adding 1 to the three members of the two inequalities $-5<x-1 \leq 5$, we get $-5+1<x-1+1 \leq 5+1$, that is, $-4<x \leq 6$. The integer values of $x$ that satisfy these two inequalities are $-3,-2,-1,0,1,2,3,4,5$ and 6.