Solve each of the following system of equations in R.

$x+3>0$

$\Rightarrow x>-3$

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

Also, $2 x<14$

$\Rightarrow x<7 \quad$ [Dividing both the sides by 2$]$

$\Rightarrow x \in(-\infty, 7) \ldots$ (ii)

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

$(-3, \infty) \cap(-\infty, 7)=(-3,7)$

$\therefore x \in(-3,7)$

Thus, the solution of the given set of inequalities is $(-3,7)$.