IPTG can be reconstituted in water. Make a stock of 100 mM in water and store working aliquots at -20°C. X-gal can be reconstituted in DMSO, or in a 50:50 mix of DMSO and water. To do the latter, you must dissolve in DMSO first, and then add water to bring up to final volume. It is not necessary to filter sterilize these solutions.
The X-gal solution should be protected from light. To make plates, add 50 ug/ml X-gal and 1 mM (0.24 mg/mL) IPTG to LB/agar that has been cooled down to 50°C. To spread on top of plates, use 50 µl 2% stock of X-gal and 30 µl 100 mM stock of IPTG.
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