$2-|\frac{3}{2x}-\frac{1}{4}|=|-\frac{5}{4}|$
$⇔|\frac{3}{2}x-\frac{1}{4}|=2-\frac{5}{4}$
$⇔|\frac{3}{2}x-\frac{1}{4}|=\frac{3}{4}$
\(⇔\left[ \begin{array}{l}\frac{3}{2}x-\frac{1}{4}=\frac{3}{4}\\\frac{3}{2}x-\frac{1}{4}=\frac{-3}{4}\end{array} \right.\)
\(⇔\left[ \begin{array}{l}\frac{3}{2}x=\frac{1}{4}+\frac{3}{4}=1\\\frac{3}{2}x=\frac{-3}{4}+\frac{1}{4}=\frac{-1}{2}\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=\frac{2}{3}\\x=\frac{-1}{3}\end{array} \right.\)
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