$$\frac { 6 x + 1 } { 3 } - \frac { 1 } { 1 } = \frac { x - 3 } { 6 }$$
$x=\frac{1}{11}\approx 0.090909091$
$$2\left(6x+1\right)-6=x-3$$
$$12x+2-6=x-3$$
$$12x-4=x-3$$
$$12x-4-x=-3$$
$$11x-4=-3$$
$$11x=-3+4$$
$$11x=1$$
$$x=\frac{1}{11}$$
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