Interfacing a PIC microcontroller to different logic levels
You seem to have a typo, as you don't have a -10V off in your problem.

In any case, if you look at the max232 datasheet, you'll notice that it's inverting-  i.e., a 1 in will give you a 0 out.  Check your devices to make sure they aren't expecting the inverted logic.  If they both are, or both aren't, you can deal with this.  If one is and one isn't, you have an issue.

In general, I don't like using voltage division to do level conversions, because if the device starts sucking or sourcing current the voltage you've so carefully calculated changes.  In most cases you won't have a problem, but you do need to keep track of things.  For example, if you were trying to light an LED with your voltage divider, your voltage would fall with the LED on, and how much it fell would depend on the values of your resistors. If you see troubles like this coming, simple transistor circuits can easily handle your level conversions.  That's assuming, of course, that all your signals are one-way.  Whole different ball of wax for bidirectional lines.