a) \(\left|\dfrac{x}{2}-\dfrac{5}{4}\right|=x-1\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{x}{2}-\dfrac{5}{4}=x-1\\\dfrac{x}{2}-\dfrac{5}{4}=-\left(x-1\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\dfrac{x}{2}-x=\dfrac{5}{4}-1\\\dfrac{x}{2}-\dfrac{5}{4}=-x+1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{x-2x}{2}=\dfrac{1}{4}\\\dfrac{x}{2}+x=\dfrac{5}{4}+1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left(x-2x\right)4=2\\\dfrac{3x}{2}=\dfrac{9}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}4x-8x=2\\12x=18\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}-4x=2\\x=\dfrac{18}{12}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{2}\\x=\dfrac{3}{2}\end{matrix}\right.\)
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