$$\frac{x-3}{9}-\frac{x-2}{10}=1-\frac{x}{12}$$
$x=12$
$$20\left(x-3\right)-18\left(x-2\right)=180-15x$$
$$20x-60-18\left(x-2\right)=180-15x$$
$$20x-60-18x+36=180-15x$$
$$2x-60+36=180-15x$$
$$2x-24=180-15x$$
$$2x-24+15x=180$$
$$17x-24=180$$
$$17x=180+24$$
$$17x=204$$
$$x=\frac{204}{17}$$
$$x=12$$
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