Solve the following system of equations in $R$ .

$2 x - 3 < 7, 2 x > - 4$

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Solution

Consider the first inequation,

$2 x - 3 < 7$

$\Rightarrow 2 x < 7 + 3$

$\Rightarrow 2 x < 10$
$\Rightarrow x < \frac{10}{2}$
$\Rightarrow x < 5$ --- (1)

Consider the second inequation,

$2 x > - 4$
$\Rightarrow x > \frac{- 4}{2}$
$\Rightarrow x > - 2$ ---(2)
from (1) and (2),
$x < 5$ and $x > - 2$
i.e., $x$ lie between $- 2$ and $5$ .
Therefore, the solution of $2 x - 3 < 7, 2 x > - 4$ is
$- 2 < x < 5$ (or) $x \in (- 2, 5)$ where, $x$ is a real number.

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