$$\frac { 2 ( x - 1 ) } { 3 } - \frac { 3 ( x - 2 ) } { 4 } = 1$$
$x=-2$
$$4\times 2\left(x-1\right)-3\times 3\left(x-2\right)=12$$
$$8\left(x-1\right)-3\times 3\left(x-2\right)=12$$
$$8x-8-3\times 3\left(x-2\right)=12$$
$$8x-8-9\left(x-2\right)=12$$
$$8x-8-9x+18=12$$
$$-x-8+18=12$$
$$-x+10=12$$
$$-x=12-10$$
$$-x=2$$
$$x=-2$$
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