Question

Solve each of the following system of equations in R. 

3x − 6 > 0, 2x − 5 > 0 

Answer 1

\[3x - 6 > 0\]
\[ \Rightarrow 3x > 6\]
\[ \Rightarrow x > 2\]
\[ \Rightarrow x \in \left( 2, \infty \right) . . . \left( i \right)\]
\[\text{ Also }, 2x - 5 > 0\]
\[ \Rightarrow 2x > 5\]
\[ \Rightarrow x > \frac{5}{2}\]
\[ \Rightarrow x \in \left( \frac{5}{2}, \infty \right) . . . \left( ii \right)\]
\[\text{ Solution of the given set of inequalities is the intersection of } \left( i \right) \text{ and } \left( ii \right) . \]
\[\left( 2, \infty \right) \cap \left( \frac{5}{2}, \infty \right) = \left( \frac{5}{2}, \infty \right)\]
\[\text{ Thus, the solution of the given set of inequalities is } \left( \frac{5}{2}, \infty \right) .\]