[SIZE=+1]The system is to use a single red-green LED to show status by indicating green if the battery voltage is above 12.2 volts, yellow if battery voltage is between 11.0 and 12.2, and indicating red if the battery voltage is below 11.0 volts.

Can anyone help me with this? I think about this about two weeks, but still lost.
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You can use comparators (such as easy-to-find LM393) for this, and set whatever voltage setpoints you want using a voltage reference and a resistive divider. You may or may not need an output transistor to then power your LEDs.

Many folks prefer the LM3914 (I think that's right), which is purpose-made IC containing lots of comparators, to give a bargraph-like output for voltage.