Question

Solve each of the following system of equations in R.

x − 2 > 0, 3x < 18 

Answer 1

\[\text{ We have }, x - 2 > 0\]
\[ \Rightarrow x > 2\]
\[ \Rightarrow x \in \left( 2, \infty \right) . . . \left( i \right)\]
\[\text{ Also }, 3x < 18\]
\[ \Rightarrow x < 6\]
\[ \Rightarrow x \in \left( - \infty , 6 \right) . . . \left( ii \right)\]
\[\text{ Solution of the given set of the inequations is intersection of } \left( i \right) \text{ and } \left( ii \right)\]
\[\left( 2, \infty \right) \cap \left( - \infty , 6 \right) = (2, 6)\]
\[\text{ Thus }, (2, 6) \text{ is the solution of the given set of inequalities } .\]