Question

Solve each of the following system of equations in R.

10. 11 − 5x > −4, 4x + 13 ≤ −11

Answer 1

We have,

$$\begin{gathered} 11-5x>-4 \\ \Rightarrow -5x>-4-11 \\ \Rightarrow -5x>-15 \\ \Rightarrow 5x<15\left[\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}-1\right] \\ \Rightarrow x<\frac{15}{5} \\ \Rightarrow x<3 \\ \Rightarrow x\in (-\infty ,3)...\left(\mathrm{i}\right) \\ \mathrm{Als}o,4x+13\le -11 \\ \Rightarrow 4x\le -11-13 \\ \Rightarrow 4x\le -24 \\ \Rightarrow x\le -6 \\ \Rightarrow x\in (-\infty ,-6]...\left(\mathrm{ii}\right) \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right). \\ (-\infty 3)\cap (-\infty ,-6]=(-\infty ,-6] \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}(-\infty ,-6]. \end{gathered}$$