as you already know, an absolute value expression is a piece-wise in effect.
[tex]\bf 9|9-8x|=2x+3\implies |9-8x|=\cfrac{2x+3}{9}\\\\\\
\begin{cases}
+(9-8x)=\cfrac{2x+3}{9}\\\\
-(9-8x)=\cfrac{2x+3}{9}
\end{cases}\\\\
-------------------------------\\\\
9-8x=\cfrac{2x+3}{9}\implies 81-72x=2x+3\implies 78=74x
\\\\\\
\cfrac{78}{74}=x\implies \cfrac{39}{37}=x\\\\
-------------------------------\\\\
-(9-8x)=\cfrac{2x+3}{9}\implies -9+8x=\cfrac{2x+3}{9}
\\\\\\
-81+72x=2x+3\implies 70x=84\implies x=\cfrac{84}{70}\implies x=\cfrac{6}{5}[/tex]
