$$\frac { x - 3 } { 9 } - \frac { x - 2 } { 10 } = \frac { 1 - x } { 12 }$$
$x = \frac{39}{17} = 2\frac{5}{17} \approx 2.294117647$
$$20\left(x-3\right)-18\left(x-2\right)=15\left(1-x\right)$$
$$20x-60-18\left(x-2\right)=15\left(1-x\right)$$
$$20x-60-18x+36=15\left(1-x\right)$$
$$2x-60+36=15\left(1-x\right)$$
$$2x-24=15\left(1-x\right)$$
$$2x-24=15-15x$$
$$2x-24+15x=15$$
$$17x-24=15$$
$$17x=15+24$$
$$17x=39$$
$$x=\frac{39}{17}$$
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