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# Solve Each of the Following System of Equations in R. 2x + 5 ≤ 0, X − 3 ≤ 0 - Mathematics

Solve each of the following system of equations in R.

2x + 5 ≤ 0, x − 3 ≤ 0

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#### Solution

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


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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.2 | Q 7 | Page 15
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