Ta có: \(A=\left|2x-2\right|+\left|2x-2013\right|\)
\(=\left|2x-2\right|+\left|2013-2x\right|\ge\left|2x-2+2013-2x\right|=2011\)
Dấu "=" xảy ra \(\Leftrightarrow\left(2x-2\right).\left(2013-2x\right)\ge0\)
\(\Leftrightarrow\left(2x-2\right).\left(2x-2013\right)\le0\)
\(\Rightarrow\hept{\begin{cases}2x-2\ge0\\2x-2013\le0\end{cases}\Rightarrow\hept{\begin{cases}2x\ge2\\2x\le2013\end{cases}}}\Rightarrow\hept{\begin{cases}x\ge1\\x\le\frac{2013}{2}\end{cases}}\)
\(\Rightarrow Min\left(A\right)=2011\Leftrightarrow1\le x\le\frac{2013}{2}\)
