Question

Solve each of the following system of equations in R.

22. |4 − x| + 1 < 3

Answer 1

$$\begin{gathered} \mathrm{We}have\left|4-x\right|+1<3 \\ \Rightarrow \left|4-x\right|<3-1 \\ \Rightarrow \left|4-x\right|<2 \\ \Rightarrow \left|x-4\right|<2 \\ \left|x-a\right|<r\Rightarrow a-r<x<a+r \\ \Rightarrow 4-2<x<4+2 \\ \Rightarrow x\in \left(2,6\right) \end{gathered}$$