If $8+3x < |8+3x|, x\in R,$ then x lies in :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\left(-∞, \frac{-8}{3}\right)$
CASE 1: $8+3x>0$
$⇒8+3x<8+3x$
$⇒0<0$
This is never true, no solution.
CASE 2: $8+3x<0$
$⇒8+3x<-(8+3x)$
$⇒8+3x+3x<-8$
$⇒6x<-16$
$⇒x<\frac{-8}{3}$