\(\left||\dfrac{1}{2}x+1\right|-\dfrac{3}{4}|=\dfrac{2}{5}\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|\dfrac{1}{2}x+1\right|-\dfrac{3}{4}=\dfrac{2}{5}\\\left|\dfrac{1}{2}x+1\right|-\dfrac{3}{4}=-\dfrac{2}{5}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left|\dfrac{1}{2}x+1\right|=\dfrac{23}{20}\\\left|\dfrac{1}{2}x+1\right|=\dfrac{7}{20}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}\dfrac{1}{2}x+1=\dfrac{23}{20}\\\dfrac{1}{2}x+1=-\dfrac{23}{20}\end{matrix}\right.\\\left[{}\begin{matrix}\dfrac{1}{2}x+1=\dfrac{7}{20}\\\dfrac{1}{2}x+1=-\dfrac{7}{20}\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=\dfrac{3}{10}\\x=-\dfrac{43}{10}\end{matrix}\right.\\\left[{}\begin{matrix}x=-\dfrac{13}{10}\\x=-\dfrac{27}{10}\end{matrix}\right.\end{matrix}\right.\)
KL..............