Relationship Between Work and Change in Volume

[Meagan Kimbrell 1I]

Could someone please clarify the relationship between work and the change in volume (delta V) as in the equation w = -P x deltaV? From my understanding, if the volume is decreased (piston is pushed inwards), the work of the system will increase and if the volume is increased (piston is pushed outwards), the work of the system will decrease? But, I am not sure so any help would be greatly appreciated!
Thanks in advance!

[Hannah Chang 1F]

Before I attempt to explain the relationship between change in volume and work, I think it's important to note that a positive value for work means that work is done on the system by the environment (aka we compress the gas); this adds energy to the system from the environment in the form of work. When the value of work is negative, that means that work is done by the system on the environment (aka the gas expands); this adds energy to the environment from the system in the form of work. To summarize:
~ W > 0 --> work done on the system --> energy added to the system in the form of work
~ W < 0 --> work done on the environment --> transfer energy to the environment in the form of work

So, if volume is decreased (the piston is pushed downwards, so we compress the gas), then that means that work is done on the system by the environment. When work is done on the system by the environment, that means that energy is added to the system from the environment in the form of work, leading to a positive value for work. Thus, a decrease in volume (aka a negative delta V) will lead to a positive work value. If the volume is increased (the piston is pushed outwards, so the gas expands), then that means that work is done by the system on the environment. When this happens, that means that energy is transferred from the system to the environment in the form of work, leading to a negative work value. Consequently, an increase in volume (aka a positive delta V) will lead to a negative work value. This is the relationship between volume change and work, and the equation W = -p * delta V aligns with this as well.