[tex]\bf |7x+10|=|x-7|\quad now\quad
\begin{array}{llll}
|7x+10|=
\begin{cases}
-(7x+10)\implies -7x-10\\
7x+10
\end{cases}\\\\
|x-7|=
\begin{cases}
-(x-7)\implies -x+7\\
x-7
\end{cases}
\end{array}
\\\\\\
\textit{so, we pick the positive scenario and one of the negative ones}
\\\\\\
7x+10=x-7\implies 6x=-17\implies \boxed{x=-\cfrac{17}{6}}\\\\
7x+10=-x+7\implies 8x=-3\implies \boxed{x=-\cfrac{3}{8}}[/tex]
