Mistake in EIV 4th edition, page 90, or mistake in my brain?

[tomslawsky]

Inequalities with ranges example problem- EIC 4th edition, page 90.

X: Lowest value = 0
Highest value = 3

Y: no lower limit
Highest value = LT8

Explanation states- Lowest value for (XY)= no lower limit because X has no lower limit

My brain says: Anything multiplied by 0 = 0
Therefore, the lower limit of (XY)= -(infinity) * (0) = 0

What am I missing here?

Thank you

[StaceyKoprince]

It gets a bit tricky when there's no lower limit for one of the variables. When that's the case, you do NOT want to multiply by the "0" lower limit of the other variable. Here's why:

let's say y = -32. Now, -32 * 0 is indeed 0. But x could also be 1, right? And what's -32 *1?

Ah. That would be -32, which is lower than 0. So the lower bound of xy is not dictated by the individual lower bound of x. Instead, it's dictated by the "no lower limit" bound of y.