Given that \(\frac{(3 - y)}{2x}\) = \(\frac{(6y + 7)}{(4x - 5)}\), find the value of...

Given that \(\frac{(3 - y)}{2x}\) = \(\frac{(6y + 7)}{(4x - 5)}\), find the value of x when y = 2

A. \(\frac{64}{5}\)
B. 6
C. \(\frac{5}{34}\)
D. \(\frac{-5}{34}\)
E. \(\frac{-64}{5}\)

Given:
\(\frac{3 - y}{2x} = \frac{6y + 7}{4x - 5}\)

Substitute y = 2

\(\frac{3 - 2}{2x} = \frac{6(2) + 7}{4x - 5} \implies \frac{1}{2x} = \frac{19}{4x - 5}\)

Cross-multiply: 1 \(\cdot\) (4x - 5) = 19 \(\cdot\) 2x
4x - 5 = 38x
-5 = 38x - 4x
-5 = 34x

x = -\(\frac{5}{34}\)

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