Confusion unequal or unequal confusion?

If a , b , x and y were non-zero positive real numbers this would be true (and would intuitively apply to many real-world applications, like comparisons of measurements). But negative numbers are possible, allowing for both a and x to be negative and their product to be equal to or larger than the product of by .

Simple counter example:

if a = -1 , b = 1, x = -1 and y = 1, then

(-1)(-1) = (1)(1)

1 = 1

Counter example: if $a = -1$ , $b = 3$ , $x = -2$ and $y = -1$ , then

$(-1)(-2)>(3)(-1)$

$2>-3$