$$5x-\frac{1}{3}(x+1)=6(x+\frac{1}{30})$$
$x=-\frac{2}{5}=-0.4$
$$5x-\frac{1}{3}x-\frac{1}{3}=6\left(x+\frac{1}{30}\right)$$
$$\frac{14}{3}x-\frac{1}{3}=6\left(x+\frac{1}{30}\right)$$
$$\frac{14}{3}x-\frac{1}{3}=6x+6\times \frac{1}{30}$$
$$\frac{14}{3}x-\frac{1}{3}=6x+\frac{6}{30}$$
$$\frac{14}{3}x-\frac{1}{3}=6x+\frac{1}{5}$$
$$\frac{14}{3}x-\frac{1}{3}-6x=\frac{1}{5}$$
$$-\frac{4}{3}x-\frac{1}{3}=\frac{1}{5}$$
$$-\frac{4}{3}x=\frac{1}{5}+\frac{1}{3}$$
$$-\frac{4}{3}x=\frac{3}{15}+\frac{5}{15}$$
$$-\frac{4}{3}x=\frac{3+5}{15}$$
$$-\frac{4}{3}x=\frac{8}{15}$$
$$x=\frac{8}{15}\left(-\frac{3}{4}\right)$$
$$x=\frac{8\left(-3\right)}{15\times 4}$$
$$x=\frac{-24}{60}$$
$$x=-\frac{2}{5}$$
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