$$\frac{ x-5 }{ 3 } = \frac{ x-3 }{ 5 } - \frac{ x }{ 2 } -1$$
$x=\frac{2}{19}\approx 0.105263158$
$$10\left(x-5\right)=6\left(x-3\right)-15x-30$$
$$10x-50=6\left(x-3\right)-15x-30$$
$$10x-50=6x-18-15x-30$$
$$10x-50=-9x-18-30$$
$$10x-50=-9x-48$$
$$10x-50+9x=-48$$
$$19x-50=-48$$
$$19x=-48+50$$
$$19x=2$$
$$x=\frac{2}{19}$$
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