Solve each of the following system of equations in R.

2*x* + 5 ≤ 0, *x* − 3 ≤ 0

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#### Solution

\[\text{ We have }, 2x + 5 \leq 0\]

\[ \Rightarrow 2x \leq - 5\]

\[ \Rightarrow x \leq \frac{- 5}{2}\]

\[ \Rightarrow x \in ( - \infty , \frac{- 5}{2}] . . . (i)\]

\[\text{ Also }, x - 3 \leq 0\]

\[ \Rightarrow x \leq 3\]

\[ \Rightarrow x \in ( - \infty , 3] . . . (ii)\]

\[\text{ Thus, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) . \]

\[( - \infty , \frac{- 5}{2}] \cap ( - \infty , 3] = ( - \infty , \frac{- 5}{2}]\]

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

\[\]

Concept: Inequalities - Introduction

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