Question

Solve each of the following system of equations in R.

18. $0<\frac{-x}{2}<3$

Answer 1

$$\begin{gathered} 0<\frac{-x}{2}<3 \\ \Rightarrow 0<-x<6(\mathrm{Multiplying}\mathrm{throughout}\mathrm{by}2) \\ \Rightarrow 0>x>-6(\mathrm{Multiplying}\mathrm{throughout}\mathrm{by}-1) \\ \Rightarrow x\in (-6,0) \\ \mathrm{Hence},\mathrm{the}\mathrm{interval}(-6,0)\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequations}. \end{gathered}$$