Question

Solve each of the following system of equation in R.

$|x+\frac{1}{3}|>\frac{8}{3}$

Answer 1

Consider the first inequation,

$x+\frac{1}{3}\ge 0\therefore ex\ge \frac{-1}{3}|x+\frac{1}{3}|-\frac{8}{3}>0x+\frac{1}{3}-\frac{8}{3}>0\frac{3x-7}{3}>03x-7>0x>\frac{7}{3}...\left(i\right)$

Consider the second inequation,

$x+\frac{1}{3}<0\therefore ex<-\frac{1}{3}|x+\frac{1}{3}-\frac{8}{3}|>0-x-\frac{1}{3}-\frac{8}{3}>0-3x-9>0-3x>93x<-9x>\frac{-9}{3}x<-3...\left(ii\right)From\left(i\right)and\left(ii\right),(-\infty ,-3)\cup (\frac{7}{3},\infty )\text{is the solution set of the simultaneous equations.}$