Why do I get sinh(-3) ≥ -3 and sinh(-3) ≤ -3 at once?

[aaaa202]

I'm given the fact that exp(y) ≥ 1 + y for all y

I will use this for sinh. Since sinh = (exp(y) - exp(-y))/2 we have for y=3 as example:

sinh(3) ≥ 3 by subtracting the two inequalities

Instead for sinh(-3) I get:

sinh(-3) ≥ -3 (1)

But something is wrong here: Because if I take the first inequality sinh(3) ≥ 3 and multiply it by (-1) and switch around the inequality sinh and using the fact that
-sinh(3) = sinh(-3) I get:

sinh(-3) ≤ -3 (2)

This is clearly weird. Which of (1) and (2) is right and why is other one wrong?

 

[Doc Al]

Careful when subtracting inequalities:

5 > 3
4 > 1

subtracting:
1 > 2 ?

 

[aaaa202]

ahh omg. Thanks LOL