|2x + 3| - 2|4 - x| = 5
\(\Leftrightarrow2x+3\ge0:x\ge-\dfrac{3}{2},\left|2x+3\right|=2x+3\)
\(\Leftrightarrow2x+3< 0:x< -\dfrac{3}{2},\left|2x+3\right|=-\left(2x+3\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< -\dfrac{3}{2}\\-\dfrac{3}{2}\le x\le4\\x>4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\varnothing\\x=\dfrac{5}{2}\\x=\varnothing\end{matrix}\right.\)
\(\Rightarrow x\in\left\{\dfrac{5}{2}\right\}\)
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