$$y- \frac{ y-5 }{ 2 } =1- \frac{ y-2 }{ 3 }$$
$y=-1$
$$6y-3\left(y-5\right)=6-2\left(y-2\right)$$
$$6y-3y+15=6-2\left(y-2\right)$$
$$3y+15=6-2\left(y-2\right)$$
$$3y+15=6-2y+4$$
$$3y+15=10-2y$$
$$3y+15+2y=10$$
$$5y+15=10$$
$$5y=10-15$$
$$5y=-5$$
$$y=\frac{-5}{5}$$
$$y=-1$$
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