$$\frac{ 1 }{ 2 } (5x7)= \frac{ 3 }{ 4 } (3x-1)$$
$x=\frac{10x_{7}}{9}+\frac{1}{3}$
$$\frac{5}{2}x_{7}=\frac{3}{4}\left(3x-1\right)$$
$$\frac{5}{2}x_{7}=\frac{9}{4}x-\frac{3}{4}$$
$$\frac{9}{4}x-\frac{3}{4}=\frac{5}{2}x_{7}$$
$$\frac{9}{4}x=\frac{5}{2}x_{7}+\frac{3}{4}$$
$$\frac{9}{4}x=\frac{5x_{7}}{2}+\frac{3}{4}$$
$$\frac{\frac{9}{4}x}{\frac{9}{4}}=\frac{\frac{5x_{7}}{2}+\frac{3}{4}}{\frac{9}{4}}$$
$$x=\frac{\frac{5x_{7}}{2}+\frac{3}{4}}{\frac{9}{4}}$$
$$x=\frac{10x_{7}}{9}+\frac{1}{3}$$
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$x_{7}=\frac{9x-3}{10}$
$$\frac{5}{2}x_{7}=\frac{9x-3}{4}$$
$$\frac{\frac{5}{2}x_{7}}{\frac{5}{2}}=\frac{9x-3}{\frac{5}{2}\times 4}$$
$$x_{7}=\frac{9x-3}{\frac{5}{2}\times 4}$$
$$x_{7}=\frac{9x-3}{10}$$
