\(\left|x+7\right|=\left|x-9\right|\)
\(\Leftrightarrow\orbr{\begin{cases}x+7=x-9\\x+7=-\left(x-9\right)=-x+9\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-x=-7-9\\x+x=-7+9\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}0=-16\left(loai\right)\\2x=2\end{cases}}\)
\(\Leftrightarrow2x=2\)
\(\Leftrightarrow x=2:2\)
\(\Leftrightarrow x=1\)