Answer to Question #152867 in Algebra for O.Weerasinghe

Question

2- |x+1|<|2x - 3| Solve the problem with the steps and mark the answers on a chart

Answer 1

$x+1=0=>x=-1$

$2x-3=0=>x=\dfrac{3}{2}$

If $x<-1:$

$2+x+1<-2x+3=>3x<0=>x<0$

Then $x<-1$

If $-1\leq x<3/2:$

$2-x-1<-2x+3=>x<2$

Then $-1\leq x<3/2$

If $x\geq3/2:$

$2-x-1<2x-3=>3x>4=>x>4/3$

Then $x>3/2$

Therefore

$x\in(-\infin, \infin)$