Answer:
Smallest positive integer value for
is,
x = 7,
Largest negative integer value for
is,
x = -8
Explanation:
If

∵ If x is a positive integer then the possible values of x = 1, 2, 3, 4, 5, 6, 7.....
Case 1 : If x < 7,

Case 2 : If x ≥ 7,

Hence, smallest positive integer value of x is 7.
Now, if

∵ If x is negative integer then the possible value of x = -1, -2, -3, -4,.....
Case 1 : if x is odd negative integer,

eg : -1, -3, -5, -7,...
Case 2 : If x is even negative integer then there are further two cases,
(i) x is more than or equal to -6,

eg x = -6, -4, -2,
(ii) x is less than -8,

eg : x = -10, -12, -14,...
Hence, the largest negative integer value that will make
is x = -8.