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Pressure is inversely proportional to volume as seen by the equation PV = nRT. Given that moles and temperature stay constant, when pressure increases, volume must decrease. It's more commonly thought of that you halve the volume to double the pressure rather than changing the pressure.
A visual way to think of this is imagining the molecules floating around in a box. If the box shrinks, but there are still the same number molecules floating around, they will push harder on the box (i.e. larger pressure).
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