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

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