$$5x19=5+3x$$
$x=\frac{5\left(x_{19}-1\right)}{3}$
$$5+3x=5x_{19}$$
$$3x=5x_{19}-5$$
$$\frac{3x}{3}=\frac{5x_{19}-5}{3}$$
$$x=\frac{5x_{19}-5}{3}$$
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$x_{19}=\frac{3x}{5}+1$
$$5x_{19}=3x+5$$
$$\frac{5x_{19}}{5}=\frac{3x+5}{5}$$
$$x_{19}=\frac{3x+5}{5}$$
$$x_{19}=\frac{3x}{5}+1$$