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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 

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Solution

We have, 

\[11 - 5x > - 4\]

\[ \Rightarrow - 5x > - 4 - 11\]

\[ \Rightarrow - 5x > - 15\]

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

\[ \Rightarrow x < \frac{15}{5} \]

\[ \Rightarrow x < 3\]

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

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

\[ \Rightarrow 4x \leq - 11 - 13\]

\[ \Rightarrow 4x \leq - 24\]

\[ \Rightarrow x \leq - 6\]

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

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

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

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

  Is there an error in this question or solution?
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APPEARS IN

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