Solve the given inequality for real x: 4x + 3 < 5x + 7

$4 x+3<5 x+7$

$\Rightarrow 4 x+3-7<5 x+7-7$

$\Rightarrow 4 x-4<5 x$

$\Rightarrow 4 x-4-4 x<5 x-4 x$

$\Rightarrow-4

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 $(-4, \infty)$.