Starting claim (at the left)
:

2x  5

< 1
Thus, 2x  5 must lie between 1 and +1, that is
:
1 < 2x  5
and
2x  5 < +1
1 + 5 < 2x  5 + 5
and
2x  5 + 5 < +1 + 5
4 < 2x
and
2x < 6
Finally, divide all sides by (+2)
:
2 < x
and
x < +3
In other words
:
2 < x < 3
Solution Set in interval notation
:
( 2, 3 )
Solution set pictured on a number line