\(\left|2x-7\right|=4x+1\) (*)
-ĐK: \(4x+1\ge0\Leftrightarrow4x\ge-1\Leftrightarrow x\ge\dfrac{-1}{4}\)
(*)\(\Leftrightarrow2x-7=4x+1\) hay \(2x-7=-4x-1\)
\(\Leftrightarrow2x-4x=1+7\) hay \(2x+4x=-1+7\)
\(\Leftrightarrow-2x=8\) hay \(6x=6\)
\(\Leftrightarrow x=-4\) (loại) hay \(x=1\) (nhận)
-Vậy \(S=\left\{1\right\}\)