please solve the equation
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$$\begin{lgathered}\frac{3}{2} (2x - 1) = \frac{1}{2} + \frac{7x}{8} \\ = > \frac{3(2x - 1)}{2} = \frac{1}{2} + \frac{7x}{8} \\ = > \frac{(6x - 3)}{2} = \frac{(4 + 7x)}{8} \\ = > 8(6x - 3) = 2(4 + 7x) \\ = > 48x - 24 = 8 + 14x \\ = > 48x - 14x = 8 + 24 \\ = > 34x = 32 \\ = > x = \frac{32}{34} \\ = > x = \frac{16}{17}\end{lgathered}$$
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