Question

Solve each of the following system of equations in R.

2. 2x − 7 > 5 − x, 11 − 5x ≤ 1

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have},2x-7>5-x \\ \Rightarrow 2x+x>5+7 \\ \Rightarrow 3x>12 \\ \Rightarrow x>4 \\ \Rightarrow x\in \left(4,\infty \right)...\left(\mathrm{i}\right) \\ \mathrm{Also},11-5x\le 1 \\ \Rightarrow 5x⩾11-1 \\ \Rightarrow x⩾2 \\ \Rightarrow x\in [2,\infty )...\left(\mathrm{ii}\right) \\ S\mathrm{olution}\mathrm{set}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequations}\mathrm{is}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right) \\ \left(4,\infty \right)\cap [2,\infty )=\left(4,\infty \right) \\ \mathrm{Thus},\mathrm{th}e\mathrm{solution}\mathrm{set}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequations}\mathrm{is}\left(4,\infty \right). \end{gathered}$$