Why am I having this error when performing arithmetic on a number value?

The issue in line 8 is that Cursor.Position.X and Cursor.Position.Y are UDim values, not integers.

So how can you actually get the integer value of the mouse's X position? Depending on what you are doing, you should either supply Cursor1Pos.Offset or Cursor1Pos.Scale

A UDim's Offset and Scale are both integer values, however the Offset is the X position's value in pixels, and the Scale is the X position's value relative to your screen resolution.

I am assuming you want to use the Offset since the Offset is based on pixels, so here is a quick fix for you:

function Click()
    if script.Parent.Parent.Parent.Cursor1InPlay.Value == true then
        script.Parent.Parent.Parent.Cursor1InPlay.Value = false
        script.Parent.Parent.Parent.Cursor2InPlay.Value = true
    elseif script.Parent.Parent.Parent.Cursor2InPlay.Value == true then
        script.Parent.Parent.Parent.Cursor2InPlay.Value = false
        local Cursor1Pos = script.Parent.Parent.Cursor1.Position.X
        local x = 24.125 - (0.100520833 * (Cursor1Pos.Offset - 7))
        workspace.PKLauncher.Orientation = Vector3.new(0,x,90)
    end
end
script.Parent.MouseButton1Click:connect(Click)

Cursor1Pos - 7 will cause an error because no operator overload allows you to subtract a UDim with an integer. You can only subtract UDims with other UDims.

Cursor1Pos.Offset - 7 will not fail because you are subtracting two integers together, which is perfectly legal in programming.

I hope this helped you.