\[\frac{2x - 3}{3} + \frac{7x - 13}{6} + \frac{5 - 2x}{2} = x - 1\ \ \ | \cdot 6\]
\[2 \cdot (2x - 3) + 7x - 13 + 3 \cdot (5 - 2x) =\]
\[= 6 \cdot (x - 1)\]
\[4x - 6 + 7x - 13 + 15 - 6x =\]
\[= 6x - 6\]
\[5x - 6x = - 6 + 4\]
\[- x = - 2\]
\[x = 2.\]