Question

Solve each of the following system of equations in R. 

3x − 1 ≥ 5, x + 2 > −1 

Answer 1

\[3x - 1 \geqslant 5\]
\[ \Rightarrow 3x \geqslant 5 + 1\]
\[ \Rightarrow x \geq 2\]
\[ \Rightarrow x \in [2, \infty ) . . . (i)\]
\[\text{ Also }, x + 2 > - 1\]
\[ \Rightarrow x > - 1 - 2\]
\[ \Rightarrow x > - 3\]
\[ \Rightarrow x \in ( - 3, \infty ) . . . (ii)\]
\[\text{ Hence, the solution of the given set of inequalities is the intersection of } (I) \text{ and } (ii) . \]
\[[2, \infty ) \cap ( - 3, \infty ) = [2, \infty )\]
\[\text{ Thus, the solution of the given set of inequalities is } [2, \infty ) . \]
\[\]