\[\frac{2x - 5}{8} - \frac{4x - 3}{7} < 1\ \ \ \ \ \ | \cdot 56\]
\[7 \cdot (2x - 5) - 8 \cdot (4x - 3) < 56\]
\[14x - 35 - 32x + 24 < 56\]
\[- 18x < 56 + 11\]
\[- 18x < 67\]
\[x > - \frac{67}{18}\]
\[x > - 3\frac{13}{18}\]
\[Наименьшее\ целое\ число:\ - 3.\]
\[Ответ:\ - 3.\]