Question

Solve the following system of inequations in $R.$

$x+3>0,2x<14$

Answer 1

Given system of inequations:

$x+3>0and2x<14$

Let us consider the first inequation.

$x+3>0$

$\Rightarrow x+3-3>0-3$

$\Rightarrow x>-3$

$\therefore x\in (-3,\infty )\dots \left(i\right)$

Now, let us consider the second inequation.

$2x<14$

Divide both the sides by 2 we get,

$\Rightarrow \frac{2x}{2}<\frac{14}{2}$

$\Rightarrow x<7$

$\therefore x\in (-\infty ,7)\dots \left(ii\right)$

From (1) and (2), we get,

$x\in (-3,\infty )\cap (-\infty ,7)$

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


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