ax-1<3, so ax<4.
To get to the next stage you need to know whether a is positive or negative.
If a>0, x<4/a; if a<0, x>4/a; if a=0 then ax=0 and 0<4 is true, but dividing both sides by zero results in an indeterminate quantity on the right side of the inequality. Therefore x<4/a only when a>0, and the two inequalities ax-1<3 and a<4/a are not equivalent.