It is given in the question that,

4x + 3 < 5x + 7

Subtracting 7 from both the sides,

4x + 3 – 7 < 5x + 7 – 7

4x – 4 < 5x

Subtracting 4x from both the sides,

4x – 4 – 4x < 5x – 4x

x > -4

∴The solutions of the given inequality are defined by all the real numbers greater than -4.

Thus, (-4, ∞) is the required solution set.