Question

Solve each of the following system of equations in R.

21. $\left|x+\frac{1}{3}\right|>\frac{8}{3}$

Answer 1

$$\begin{gathered} \left|x+\frac{1}{3}\right|>\frac{8}{3} \\ \mathrm{We}\mathrm{know}\mathrm{that}\left|x-a\right|>r \\ \Rightarrow x<a-r\mathrm{or}x>a+r \\ \Rightarrow x<-\frac{1}{3}-\frac{8}{3}\mathrm{or}x>-\frac{1}{3}+\frac{8}{3} \\ \Rightarrow x<-3\mathrm{or}x>\frac{7}{3} \\ \Rightarrow x\in \left(-\infty ,-3\right)\cup \left(\frac{7}{3},\infty \right) \end{gathered}$$