\(A=\left|x-\frac{3}{7}\right|+\left|x+\frac{9}{7}\right|\\ A=\left|\frac{3}{7}-x\right|+\left|x+\frac{9}{7}\right|\)
Có \(\left|\frac{3}{7}-x\right|\ge\frac{3}{7}-x\text{ với mọi }x\)
\(\left|x+\frac{9}{7}\right|\ge x+\frac{9}{7}\text{ với mọi }x\)
\(\Rightarrow A\ge\frac{3}{7}-x+x+\frac{9}{7}=\frac{12}{7}\text{ với mọi }x\)
Vậy GTNN của \(A=\frac{12}{7}\)
\("="\Leftrightarrow\left\{{}\begin{matrix}\left|\frac{3}{7}-x\right|=\frac{3}{7}-x\\\left|x+\frac{9}{7}\right|=x+\frac{9}{7}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\frac{3}{7}-x\ge0\\x+\frac{9}{7}\ge0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\le\frac{3}{7}\\x\ge\frac{-9}{7}\end{matrix}\right.\\ \Leftrightarrow\frac{-9}{7}\le x\le\frac{3}{7}\)
