Question: Compound Inequalities in Maple 18

Here's an example compound inequality I'm working on.

Working it out manually.... 

Compound Inequality
4477.25 <= 4477.25+.25*(t-32450) <= 16042.25;

Distribute the coefficient
4477.25 <= 4477.25+.25*t - 8112.50 <= 16042.25;

Combine like terms
4477.25 <= -3635.25+.25*t <= 16042.25;

Add 3635.25 to all sides
8112.50 <= .25*t <= 19677.50;

Divide all sides by .25
32450 <= t <= 78710;

How can I ask Maple to simplify this compound inequality? Obviously this is not the correct syntax, It seems Maple doesn't understand what I want it to do.

4477.25 <= 4477.25 + .25 * (t-32450) <= 16042.25;

                       0.00 <= 0.25 t - 8112.50 and 0.25 t <= 19677.50                (112)

Also is there a way to ask Maple to only perform one step? In the above example, is it possible to ask Maple to "Distribute the .25", then show the result, next ask it to combine like terms, etc?