$$\frac{2x6+2}{5}=\frac{4x-7}{6}$$
$x=\frac{3x_{6}}{5}+\frac{47}{20}$
$$6\left(2x_{6}+2\right)=5\left(4x-7\right)$$
$$12x_{6}+12=5\left(4x-7\right)$$
$$12x_{6}+12=20x-35$$
$$20x-35=12x_{6}+12$$
$$20x=12x_{6}+12+35$$
$$20x=12x_{6}+47$$
$$\frac{20x}{20}=\frac{12x_{6}+47}{20}$$
$$x=\frac{12x_{6}+47}{20}$$
$$x=\frac{3x_{6}}{5}+\frac{47}{20}$$
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$x_{6}=\frac{5x}{3}-\frac{47}{12}$
$$12x_{6}=20x-35-12$$
$$12x_{6}=20x-47$$
$$\frac{12x_{6}}{12}=\frac{20x-47}{12}$$
$$x_{6}=\frac{20x-47}{12}$$
$$x_{6}=\frac{5x}{3}-\frac{47}{12}$$
