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Solve each of the following system of equations in R.

2*x* − 3 < 7, 2*x* > −4

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#### Solution

\[3x - 6 > 0\]

\[ \Rightarrow 3x > 6\]

\[ \Rightarrow x > 2\]

\[ \Rightarrow x \in \left( 2, \infty \right) . . . \left( i \right)\]

\[\text{ Also }, 2x - 5 > 0\]

\[ \Rightarrow 2x > 5\]

\[ \Rightarrow x > \frac{5}{2}\]

\[ \Rightarrow x \in \left( \frac{5}{2}, \infty \right) . . . \left( ii \right)\]

\[\text{ Solution of the given set of inequalities is the intersection of } \left( i \right) \text{ and } \left( ii \right) . \]

\[\left( 2, \infty \right) \cap \left( \frac{5}{2}, \infty \right) = \left( \frac{5}{2}, \infty \right)\]

\[\text{ Thus, the solution of the given set of inequalities is } \left( \frac{5}{2}, \infty \right) .\]

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