It sounds simple, but i'd like to rememebr the rules when we handle greater than and less than.
for example, the problem below:
If x2 < 9 and −2 < y < 1, then which of the following is true
x < 3y
3x < 2y
2x > −3y
xy < 6
−xy > 6
My question is not about how to solve it ( the answer is the one before the last) but rather to ask, how could i prove this without having to plug in numbers?
for example, the problem stat -3 < x < 3 and -2< y < 1
I thought of multiplying the 2 together but there's a paradox. -3 * -2 < xy< 3*1 = 6 < xy<3 which makes no sense. so what are the rules when combining two sets of ranges together?
Thanks
for example, the problem below:
If x2 < 9 and −2 < y < 1, then which of the following is true
x < 3y
3x < 2y
2x > −3y
xy < 6
−xy > 6
My question is not about how to solve it ( the answer is the one before the last) but rather to ask, how could i prove this without having to plug in numbers?
for example, the problem stat -3 < x < 3 and -2< y < 1
I thought of multiplying the 2 together but there's a paradox. -3 * -2 < xy< 3*1 = 6 < xy<3 which makes no sense. so what are the rules when combining two sets of ranges together?
Thanks
