\[\frac{2x}{3} - \frac{2x + 1}{6} = \frac{3x - 5}{4}\ \ \ \ \ \ \ | \cdot 12\]
\[4 \cdot 2x - 2 \cdot (2x + 1) = 3 \cdot (3x - 5)\]
\[8x - 4x - 2 = 9x - 15\]
\[4x - 9x = - 15 + 2\]
\[- 5x = - 13\]
\[x = \frac{13}{5} = 2\frac{3}{5}\]
\[x = 2,6.\]