Question

|3x+2|<1 then x belong to

Answer 1

Here is the same type of question with different values. Hope you will understand
||x−2|−3|>1||x−2|−3|>1, then xx belongs to which interval
Answer
:Ok, so |x−2|=p|x−2|=p, and so |p−3|>1|p−3|>1.

Then that means p−3>1p−3>1 or p−3<−1p−3<−1.

Then that means p>4p>4 or p<2p<2.

But p=|x−2|p=|x−2|, so |x−2|>4|x−2|>4 or |x−2|<2|x−2|<2.

That means either x−2>4x−2>4 or x−2<−4x−2<−4 or −2<x−2<2−2<x−2<2.

That means either x>6x>6 or x<−2x<−2 or 0<x<40<x<4.

Notice that the last set of inequalities (the 0<x<40<x<4 one) is an and. Your answer isn't represented exactly like this. You wrote "x>0x>0 or x<4x<4" but that's different than writing 0<x<40<x<4.