$
\begin{array}{l}
{\left|{\frac{\mathrm{{-}}{2}}{\mathrm{x}}}\right|\mathrm{{-}}\left|{\frac{1}{2}\mathrm{{-}}{\mathrm{x}}}\right|{\mathrm{<}}{0}}\\
{\hspace{0.33em}\hspace{0.33em}\mathrm{\Leftrightarrow}\left|{\frac{\mathrm{{-}}{2}}{\mathrm{x}}}\right|{\mathrm{<}}\left|{\frac{1}{2}\mathrm{{-}}{\mathrm{x}}}\right|}\\
{\hspace{0.33em}\hspace{0.33em}{TH}_{1}{\mathrm{:}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\frac{\mathrm{{-}}{2}}{\mathrm{x}}{\mathrm{<}}\frac{1}{2}\mathrm{{-}}{x}}\\
{\hspace{0.33em}\hspace{0.33em}\mathrm{\Leftrightarrow}\mathrm{\frac{{-}{2}}{x}}\mathrm{{-}}\mathrm{\frac{1}{2}}\mathrm{{+}}{x}{\mathrm{<}}{0}}\\
{\hspace{0.33em}\hspace{0.33em}\mathrm{\Leftrightarrow}\mathrm{\frac{{-}{4}{-}{x}{+}{2}{x}^{2}}{2x}}{\mathrm{<}}{0}}\\
{\hspace{0.33em}\hspace{0.33em}{BXD}{\mathrm{:}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\rightarrow}\mathrm{\forall}{x}{\mathrm{(}}\mathrm{{-}}\mathrm{\infty}{\mathrm{;}}\frac{{1}\mathrm{{-}}\sqrt{\mathrm{33}}}{4}{\mathrm{)}}\mathrm{\cup}{\mathrm{(}}{0}{\mathrm{;}}\frac{{1}\mathrm{{+}}\sqrt{\mathrm{33}}}{4}{\mathrm{)}}}\\
{\hspace{0.33em}\hspace{0.33em}{TH}_{2}{\mathrm{:}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\frac{{-}{2}}{x}}{\mathrm{>}}{x}\mathrm{{-}}\mathrm{\frac{1}{2}}}\\
{\hspace{0.33em}\hspace{0.33em}\mathrm{\Leftrightarrow}\mathrm{\frac{{-}{2}}{x}}\mathrm{{-}}{x}\mathrm{{+}}\mathrm{\frac{1}{2}}{\mathrm{>}}{0}}\\
{\hspace{0.33em}\hspace{0.33em}\mathrm{\Leftrightarrow}\mathrm{\frac{{-}{4}{-}{2}{x}^{2}{+}{x}}{2x}}{\mathrm{>}}{0}}\\
{\hspace{0.33em}\hspace{0.33em}{BXD}{\mathrm{:}}}\\
{\hspace{0.33em}\hspace{0.33em}\mathrm{\rightarrow}\mathrm{\forall}{x}{\mathrm{(}}\mathrm{{-}}\mathrm{\infty}{\mathrm{;}}{0}{\mathrm{)}}}
\end{array}
$
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