|2x−3|<|x+5| ⇒‌‌±(2x−3)<±(x+5).....(i) First we take positive sign and negative sign on both sides, $⇒ \;\; 2 x-3⇒‌‌x<8.....(ii) −(2x−3)<−(x+5) ⇒‌‌2x−3>x+5 ⇒‌‌x>8.....(iii) Now, we take negative sign in RHS and positive in LHS, ⇒‌‌2x−3<−x−5 ⇒‌‌3x<−2 ⇒‌‌x<−‌
2
3
......(iv) and we take negative sign LHS and positive in RHS ⇒‌‌−(2x−3)<x+5 ⇒‌‌−2x+3<x+5 ⇒‌‌−2<3x ⇒‌‌−2/3<x.......(v) From Eqs. (ii) and (v), −2/3<x<8 ⇒‌‌x∈(−2/3,8) From Eqs. (iii) and (iv), x∈(−∞,−2/3)∪(8,∞)