Here's a fairly simple technique to achieve a directional fade-in. Using this method, you can fade any object into view from any direction.
Start a new movie. Use Insert > Frame to put
in about 20 frames.
Type in some text.

The next step is to make a 'mask' which is used to hide
and gradually reveal the text. Insert a new graphic (Insert > New Symbol
and select Graphic).
Start by drawing two identical rectangles. Fill one with white (to match your
movie's background color).

The second rectangle needs a special colour gradient.
Open the Color dialog (Window > Colors) and go to the gradient tab.
For the left side of the gradient, choose white with 100% Alpha (solid white).
For the right side, use white with 0% Alpha (totally transparent). Click on
'New' to save this gradient to the palette.
Use this special gradient to fill the other rectangle

To complete the symbol, remove the borders from the two rectangles and move
them together so that they form a single shape.
In the picture I've set the movie background to grey so you can see what
the shape looks like.

Next comes the animation. Create a new layer above the
text layer. Open the library (Ctrl-L) and drag a copy of the rectangular
mask onto the Stage.
Stretch the mask horizontally so that it is at least twice the length of the
text.
Position the rectangle so that the solid white half covers the text.

Insert a keyframe at frame 20. Then drag the rectangle
left until it is past the left side of the text.
Finally, tween the motion of the rectangle (Right-click on the frame in the
timeline and select 'Create Motion Tween')

And that's it. Run the animation!
It should look something like this...
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