Solve the given inequality for real $x: 4 x+3<5 x+7$
$4 x+3<5 x+7$
$\Rightarrow 4 x+3-7<5 x+7-7$
$\Rightarrow 4 x-4<5 x$
$\Rightarrow 4 x-4-4 x<5 x-4 x$
Thus, all real numbers $x$, which are greater than $-4$, are the solutions of the given inequality.
Hence, the solution set of the given inequality is $(-4, \infty)$.