To solve this equation we need to remember that:
[tex]\lvert x\rvert=a\Leftrightarrow x=\pm a[/tex]Then we have that:
[tex]\begin{gathered} \lvert2x-9\rvert=11 \\ 2x-9=\pm11 \\ 2x=9\pm11 \\ x=\frac{9\pm11}{2} \\ \text{then} \\ x=\frac{9+11}{2}=\frac{20}{2}=10 \\ \text{ or } \\ x=\frac{9-11}{2}=-\frac{2}{2}=-1 \end{gathered}[/tex]Therefore x=10 or x=-1
