Solve each of the following system of equations in R. 6. 2x − 3 < 7,
Question:

Solve each of the following system of equations in R.

6. 2x − 3 < 7, 2x > −4

Solution:

$2 x-3<7$

$\Rightarrow 2 x<7+3$

$\Rightarrow x<5$

$\Rightarrow x \in(-\infty, 5) \quad \ldots(\mathrm{i})$

Also, $2 x>-4$

$\Rightarrow x>-2$

$\Rightarrow x \in(-2, \infty) \quad \ldots$ (ii)

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

$(-\infty, 5) \cap(-2, \infty)=(-2,5)$

Thus, the solution of the given set of inequalities is $(-2,5)$.

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