Follow the same procedure I outlined in your last question.
using MarkFL2's clever approach, note that |a| = √(a2).
so |1-x| < |2x-5| is the same as:
√(1-x)2 < √(2x-5)2
squaring both sides:
(1-x)2 < (2x-5)2
1-2x+x2 < 4x2-20x+25
0 < 3x2-18x+24
0 < x2-6x+8
0 < (x-2)(x-4) <---for this to be true, both factors must be either both positive, or both negative.