$f\left( \left| 3x-5 \right| \right)-f\left( \left| 2x+3 \right| \right)\ge 0\Rightarrow f\left( \left| 3x-5 \right| \right)\ge f\left( \left| 2x+3 \right| \right)$  $\xrightarrow{f}\left| 3x-5 \right|\le \left| 2x+3 \right|\to {{\left( 3x-5 \right)}^{2}}\le {{(2x+3)}^{2}}\Rightarrow {{\left( 3x-5 \right)}^{2}}-{{\left( 2x+3 \right)}^{2}}\le 0$  $\Rightarrow (3x-5-2x-3)(3x-5+2x+3)\le 0\Rightarrow \left( x-8 \right)\left( 5x-2 \right)\le 0\Rightarrow \frac{2}{5}\le x\le 8\Rightarrow x=1,2,3,4,5,6,7,8$ (8 عدد صحیح)