Enzymes can increase the rate of exergonic reactions, but are never involved in endergonic reactions...? I know exergonic are spontaneous and do not require an energy input, while an endergonic reaction is nonspontaneous and does require energy input... right? So would that make this answer correct?
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False.
Just because something is endergonic or exogonic does not mean it is spontaneous or non-spontaneous!
It is important to look at the temperature and the entropy of a reaction, not just whether it releases or uses energy.
Because both exergonic and endergonic reactions can be spontaneous under the right conditions, and an enzyme would reduce the activation energy, enzymes can increase the rate of both the reaction types.