$$\frac{ y-1 }{ 2 } - \frac{ y-3 }{ 4 } \geq \frac{ y-2 }{ 3 } -y$$
$y\geq -1$
$$6\left(y-1\right)-3\left(y-3\right)\geq 4\left(y-2\right)-12y$$
$$6y-6-3\left(y-3\right)\geq 4\left(y-2\right)-12y$$
$$6y-6-3y+9\geq 4\left(y-2\right)-12y$$
$$3y-6+9\geq 4\left(y-2\right)-12y$$
$$3y+3\geq 4\left(y-2\right)-12y$$
$$3y+3\geq 4y-8-12y$$
$$3y+3\geq -8y-8$$
$$3y+3+8y\geq -8$$
$$11y+3\geq -8$$
$$11y\geq -8-3$$
$$11y\geq -11$$
$$y\geq \frac{-11}{11}$$
$$y\geq -1$$
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