Question

Find integral values of $x$ satisfying the inequality $\left|\frac{2}{x-13}\right|>\frac{8}{9}$

Answer 1

$\left|\frac{2}{x-13}\right|>\frac{8}{9}$

let $x-13>0$

$=>\frac{2}{x-13}>\frac{8}{9}$

$=>18>8x-104$

$=>18+104>8x$

$=>8x<122$

$=>x<\frac{122}{8}$

$=>x<\frac{61}{4}$

$=>x<15.25$

If $=>x-13<0$

$=>-\frac{2}{x-13}>\frac{8}{9}$

$=>18<-8x+104$

$=>18-104<-8x$

$=>-8x>-86$

$=>x>\frac{86}{8}$

$=>x>\frac{43}{4}$

$=>x>10.75$

Here, $xϵ(10.75,13)\cup (13,15.25)$