# Solve Each of the Following System of Equations in R. 11 − 5x > −4, 4x + 13 ≤ −11 - Mathematics

Solve each of the following system of equations in R.

11 − 5x > −4, 4x + 13 ≤ −11

#### Solution

We have,

$11 - 5x > - 4$

$\Rightarrow - 5x > - 4 - 11$

$\Rightarrow - 5x > - 15$

$\Rightarrow 5x < 15 \left[ \text{ Multiplying both sides by }- 1 \right]$

$\Rightarrow x < \frac{15}{5}$

$\Rightarrow x < 3$

$\Rightarrow x \in ( - \infty , 3) . . . (i)$

$\text{ Also }, 4x + 13 \leq - 11$

$\Rightarrow 4x \leq - 11 - 13$

$\Rightarrow 4x \leq - 24$

$\Rightarrow x \leq - 6$

$\Rightarrow x \in ( - \infty , - 6] . . . (ii)$

$\text{ Hence, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) .$

$( - \infty 3) \cap ( - \infty , - 6] = ( - \infty , - 6]$

$\text{ Hence, the solution of the given set of inequalities is } ( - \infty , - 6] .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.2 | Q 10 | Page 15