2x + 6 ≥ 0, 4x − 7 < 0

We have, $2 x+6>0$

$\Rightarrow 2 x \geqslant-6$

$\Rightarrow x \geqslant-3$

$\Rightarrow x \in[-3, \infty) \ldots(\mathrm{i})$

Also, $4 x-7<0$

$\Rightarrow 4 x<7$

$\Rightarrow x<\frac{7}{4}$

$\Rightarrow x \in\left(-\infty, \frac{7}{4}\right) \ldots(\mathrm{ii})$

Thus, the solution of the given inequations is the intersection of (i) and (ii).

$[-3, \infty) \cap\left(-\infty \frac{7}{4}\right)=\left[-3, \frac{7}{4}\right)$

Thus, the solution of the given inequations is $\left[-3, \frac{7}{4}\right)$.