Verified answer

[tex]\frac{x-3}{3} -\frac{x+2}{5} =-1\frac{8}{15} \\ 5(x - 3) - 3(x + 2) = - 8 \\ 5x - 15 - 3x - 6 = - 8 \\ 2x = 21 - 8 \\ x = 13[/tex]