Question

Solve each of the following system of equations in R.

20. −5 < 2x − 3 < 5

Answer 1

$$\begin{gathered} -5<2x-3<5 \\ \Rightarrow -5+3<2x<5+3\left(\mathrm{Adding}3\mathrm{throughout}\right) \\ \Rightarrow -2<2x<8 \\ \Rightarrow -1<x<4\left(\mathrm{Dividing}\mathrm{throughout}\mathrm{by}2\right) \\ \Rightarrow x\in \left(-1,4\right) \end{gathered}$$

Hence, the interval ($-$1,4) is the solution of the given set of inequaltions.