To solve this inequality, we first need to rewrite it in exponential form.

Given: Log_1/2 (2x + 1) > -2

Using the definition of logarithms, we can rewrite this inequality as:

1/2^(-2) > 2x + 1

2^2 > 2x + 1

4 > 2x + 1

Subtracting 1 from both sides gives:

3 > 2x

Dividing by 2 gives:

3/2 > x

Therefore, the solution to the inequality is x > 3/2.