Re: Suppose that |x| < |y + 2| < |z|. Suppose further that y >
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05 Sep 2022, 08:57
Assume y=10.
We also know x and z are either both negative or both positive, since xz>0.
And then we have the big inequality given by the problem.
a. y=10, x=11, z=13 --> yes, possible
b. y=10, x=5, z=13 --> yes, possible
c. If x and z are both negative, the large inequality in the problems tells us that that z needs to be further from zero than x, in which case z will be more negative, or less than x. --> no, this option is not possible
d. y=10, x = -11, z = -13 --> yes, possible
e. y=10 --> y+1.5 = 11.5 and y+2 = 12, so we could have x=11.75, z=13 --> yes, possible