10. The solution set of the inequality $\left|\frac{1}{\log _{\frac{1}{2}} x}+2\right|>\frac{3}{2}$ is
$$
(0,1) \cup\left(1,2^{\frac{2}{7}}\right) \cup(4,+\infty)
$$
10.【Analysis and Solution】From the appearance, this is an absolute value inequality. First, find $\log _{\frac{1}{2}} x0$.
Thus $x>4$, or $1<x<2^{\frac{2}{7}}$, or $0<x<1$.