$$6x=\frac{2}{3}(2x+7)$$
$x=1$
$$6x=\frac{2}{3}\times 2x+\frac{2}{3}\times 7$$
$$6x=\frac{2\times 2}{3}x+\frac{2}{3}\times 7$$
$$6x=\frac{4}{3}x+\frac{2}{3}\times 7$$
$$6x=\frac{4}{3}x+\frac{2\times 7}{3}$$
$$6x=\frac{4}{3}x+\frac{14}{3}$$
$$6x-\frac{4}{3}x=\frac{14}{3}$$
$$\frac{14}{3}x=\frac{14}{3}$$
$$x=\frac{14}{3}\times \frac{3}{14}$$
$$x=1$$
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