\[\frac{6x - 1}{14} - \frac{x + 1}{4} = 1\ \ \ \ \ \ \ | \cdot 28\]
\[2 \cdot (6x - 1) - 7 \cdot (x + 1) = 28\]
\[12x - 2 - 7x - 7 = 28\]
\[5x = 28 + 9\]
\[5x = 37\]
\[x = 7,4.\]