Question

Solve each of the following system of equations in R. 

2x + 5 ≤ 0, x − 3 ≤ 0 

Answer 1

\[\text{ We have }, 2x + 5 \leq 0\]
\[ \Rightarrow 2x \leq - 5\]
\[ \Rightarrow x \leq \frac{- 5}{2}\]
\[ \Rightarrow x \in ( - \infty , \frac{- 5}{2}] . . . (i)\]
\[\text{ Also }, x - 3 \leq 0\]
\[ \Rightarrow x \leq 3\]
\[ \Rightarrow x \in ( - \infty , 3] . . . (ii)\]
\[\text{ Thus, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) . \]
\[( - \infty , \frac{- 5}{2}] \cap ( - \infty , 3] = ( - \infty , \frac{- 5}{2}]\]
\[\text{ Thus, the solution of the given set of inequalities is } ( - \infty , \frac{- 5}{2}] . \]
\[\]