Plotting inequality in Mathematica [closed]

I want to get a pictorial view of the condition (x-y)(4z^2-xy)>0. Had there been only two variables, a 3D plot would have worked, but what can one do with three variables?

Clear["Global`*"]

rgn = ImplicitRegion[(x - y) (4 z^2 - x*y) > 0 && -6 < x < 6 && -6 <
y < 6 && -6 < z < 6, {x, y, z}];

Region[rgn, Axes -> True, Boxed -> True,
AxesLabel -> (Style[#, 14] & /@ {x, y, z})]

RegionPlot3D[(x - y) (4 z^2 - x*y) > 0,
{x, -6, 6}, {y, -6, 6}, {z, -6, 6},
Axes -> True, Boxed -> True,
AxesLabel -> (Style[#, 14] & /@ {x, y, z}),
PlotPoints -> 75]

• Yep. I also like PlotStyle ->Opacity[0.5] to better see otherwise hidden contours. Jun 8, 2023 at 23:19

Here we follow the suggestion by @DavidG.Stork, but only change the opacity of the boundary of the cube, not the hidden contours.

changeBoundary =
Insert[#, FaceForm[Directive[Opacity[.5], Cyan]],
Position[#, GraphicsGroup[_]] // Last] &;
RegionPlot3D[(x - y) (4 z^2 - x*y) > 0, {x, -6, 6}, {y, -6,
6}, {z, -6, 6}, PlotPoints -> 80, Mesh -> None,
ViewPoint -> {-1.8, -2.3, 1.7}] // changeBoundary