Is z > 0? ; Algebra page 149 #3

[EricC370]

3. Is z >0?

(1) (z+1)(z)(z-1) < 0
(2) |z| < 1

Answer: C

I understand the explanation when you plug the given test cases and find that 'z' has to be positive. However, I began this question by trying to simplify statement (1) into a special quadratic [(z^2)-1)(z)] < 0 which turns into z^3 < 1. If you continue with this new statement, then it does not eliminate values for 'z' that are less than zero.

Can you please explain why simplifying (or the reverse if you see it that way) would eliminate possible solutions? Is there a general rule we can follow that provides guidance on when you can not combine?

Thanks,
Eric

[RonPurewal]

However, I began this question by trying to simplify statement (1) into a special quadratic [(z^2)-1)(z)] < 0 which turns into z^3 < 1.

nope.
purple thing times purple thing is z, not 1.
so the red thing isn't '1'; it's 'z'.

thus you have z^3 < z... which is entirely valid, but not especially helpful.

in fact, if you were given z^3 < z and asked to solve it algebraically, you'd do that by doing this whole process exactly backward—i.e., by moving everything to one side and then factoring into (z + 1)(z)(z - 1) < 0.

[EricC370]

Ah I see. Thank you very much. Careless mistake I tend to do, I always just forget one of the terms.

Cheers.

[tim]

[SherryK835]

Hi,
I am confused as how to get to the answer C.

for (1), it simplifies to
((z^2)-1)z<0
(z^2)-1<0
z^2<1
z<+-1
z<1
So (1) is insufficient

for (2)
|z|<1 means
-1<z<1
so (2) is insufficient

How do they work together to be sufficient to determine if z>0?

[RonPurewal]

Hi,
I am confused as how to get to the answer C.

for (1), it simplifies to
((z^2)-1)z<0
(z^2)-1<0

you made EXACTLY the same mistake as the first person in this thread. please read the thread.