Solve $|2x−3| < |x+5|$ I've tried solving $$|2x-3|=|x+5|$$ but the same method does not look applicable here.
$$2x-3 = x+5, \text{if}\; x>3/2$$
$$2x-3= -(x+5), \text{if} \; x<3/2$$
This method was not working here.

There are two nodes $x=3/2$ and $x=-5$, so we have to consider the in-equation $|2x-3|< |x+5|$ in three regions three regions
I: $x\le -5 \implies 3-2x<-(x+5) \implies x>8$ (A contradiction).
II:$-5 <x\le 3/2 \implies 3-2x<x+5 \implies x>-2/3 \implies -2/3<x\le 3/2$
III: $x>3/2 \implies 2x-3 <x+5 \implies x<8 \implies 3/2<x \le 8$
Finally, by combining I and II we get the total solution as $x\in (-2/3,8].$
