$$4x+5=9+5m$$
$m=\frac{4\left(x-1\right)}{5}$
$$9+5m=4x+5$$
$$5m=4x+5-9$$
$$5m=4x-4$$
$$\frac{5m}{5}=\frac{4x-4}{5}$$
$$m=\frac{4x-4}{5}$$
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$x=\frac{5m}{4}+1$
$$4x=9+5m-5$$
$$4x=4+5m$$
$$4x=5m+4$$
$$\frac{4x}{4}=\frac{5m+4}{4}$$
$$x=\frac{5m+4}{4}$$
$$x=\frac{5m}{4}+1$$
