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Question
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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