Inequality doubt

ans of first ques
x belongs to ( -∞ , -2/3 ] U [ 1/2 , ∞ )

b)|x+3|>|2x-1|

|x+3||2x-1| >1

|x+32x-1|>1

you may try squaring it and applying quadratic

or do this

|x+32x-1|>1 means

x+32x-1>1

or x+32x-1<1

Sorry but u r wrong

@RAHUL

i give u a PERFECT ALWAYS WORKING RULE FOR "MODULUS" or in that case for any "PIECEWISE"...defined inequality

break the inequality according to domain of its definiton and solve each piece.if solutions satisy the domain they are accepted if not they are rejected!

that's it!

for second............

try solving it by quadratic.......

I was completely correct except that i made a typing mistake(which is easily seen)

In the last line it will be x+32x-1<-1

breaking the inequality of course gives the result but takes a lot of time. Better u give stress on

properties of modulus and inequalities.