How does one properly solder a 10 AWG copper stranded wire with an 18 AWG copper stranded wire. There are plenty of tutorials on how to solder same gauge wire, but what is the recommended way to solder wires that are significantly different AWG?
If the wires are for low voltage application such as connecting 12V up to LED Strip lighting then you should consider just using twist on wire connectors instead of soldering. These have a decided advantage in that they can be removed for future wire changes and they provide an insulated cover over the wire join.
To keep strain off the low voltage wiring connections you can zip tie the two wire cables together over the cable jacket a couple of inches from the end of the jackets.
For low voltage applications, fan out the copper strands and then twist them together. Use rosin core solder. Tin the soldering gun (i.e, melt a little solder on it). Heat the copper and apply solder to the side opposite the heating implement. Let the solder melt and flow over the wires. (Melting on the side opposite the heat guarantees that the solder will really adhere to the copper, rather than just coat the outside.) Remove the heat and let it cool before moving it. You might want to slip a piece os shrink wrap tubing over one of the wires before you attach the wires. Then you can slip the shrink wrap over the solder connection and heat it so the shrink wrap tube shrinks.