Question

`|2/3 x+1|=3x-6`

Answer 1

\(\left|\dfrac{2}{3}x+1\right|=3x-6\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{3}x+1=3x-6\\\dfrac{2}{3}x+1=-\left(3x-6\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{3}x+1-3x+6=0\\\dfrac{2}{3}x+1+3x-6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{15}{11}\end{matrix}\right.\)