Question

Absolute value equation
z-10=|7z|-16

Answer 1

we have to consider two cases, namely:
\[\Large \begin{gathered}
\left\{ \begin{gathered}
z - 10 = 7z - 16 \hfill \\
z \geqslant 0 \hfill \\
\end{gathered} \right. \hfill \\
\hfill \\
\left\{ \begin{gathered}
z - 10 = - 7z - 16 \hfill \\
z < 0 \hfill \\
\end{gathered} \right. \hfill \\
\end{gathered} \]