Question

Solve each of the following system of equations in R.

13. 2 (x − 6) < 3x − 7, 11 − 2x < 6 − x

Answer 1

$$\begin{gathered} 2\left(x-6\right)<3x-7 \\ \Rightarrow 2x-12<3x-7 \\ \Rightarrow 3x-7>2x-12 \\ \Rightarrow 3x-2x>-12+7 \\ \Rightarrow x>-5 \\ \Rightarrow x\in \left(-5,\infty \right)...\left(\mathrm{i}\right) \\ \mathrm{Also},11-2x<6-x \\ \Rightarrow 6-x>11-2x \\ \Rightarrow 2x-x>11-6 \\ \Rightarrow x>5 \\ \Rightarrow x\in \left(5,\infty \right)...\left(\mathrm{ii}\right) \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{inequation}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right). \\ \left(-5,\infty \right)\cap \left(5,\infty \right)=\left(5,\infty \right) \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{inequation}\mathrm{is}\left(5,\infty \right). \end{gathered}$$