Solve the given inequality for real x: 3x – 7 > 5x – 1

$3 x-7>5 x-1$

$\Rightarrow 3 x-7+7>5 x-1+7$

$\Rightarrow 3 x>5 x+6$

$\Rightarrow 3 x-5 x>5 x+6-5 x$

$\Rightarrow-2 x>6$

$\Rightarrow \frac{-2 x}{-2}<\frac{6}{-2}$

$\Rightarrow x<-3$

Thus, all real numbers $x$, which are less than $-3$, are the solutions of the given inequality.

Hence, the solution set of the given inequality is $(-\infty,-3)$.