Number of positive integral values of x satisfies the equation $\log _{\frac{1}{2}}|x+1|^3 <\log _{\frac{1}{2}} 4$ is:

2

Since base of log both the sides is same and lying between 0 and 1 hence inequality will change and |x + 1| < 4

⇒ −4 < x + 1 < 4 ⇒ −5 < x < 3. Hence positive integral values of x are 1 and 2.

Hence (2) is the correct answer.