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You always use w=Pex x (delta)V for an irreversible expansion because the change in volume is measurable. For a reversible process you use the other equation because the change in volume is infinitestimally small. For the reversible expansion, pressure falls as the volume increases which is reflected by the nRT part of the equation from PV=nRT.
I'm not exactly sure of the derivations for both, but I would just correlate each equation to irreversible and reversible respectively. Just know which of those equations to use given its reversible or not.
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