Problem solving OG 12. Experts please help me understand

[arpan307]

If 4< (7-x)/3, which of the following must be true?

I. 5<x
II. |x+3| > 2
III. -(x+5) is positive


Options :
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III


The OA is D. I didn't get how to evaluate II condition. Experts kindly help on modulus.

[Frankenstein]

Hi,
if |y| < a then -a < y < a
if |y| > a then y < -a or y > a where a is a positive number
So, here is how we evaluate II
|x+3| > 2.
So, x+3 < -2 or x+3 > 2
So, x < -5 or x > -1

[Bens4vcobra]

Hi,
if |y| < a then -a < y < a
if |y| > a then y < -a or y > a where a is a positive number
So, here is how we evaluate II
|x+3| > 2.
So, x+3 < -2 or x+3 > 2
So, x < -5 or x > -1

I understand II but I can't see how III must be true. Could you demonstrate?

If x < -5 from the given expression, then how is it that -(x+5)'must be positive?'

[Frankenstein]

If x < -5 from the given expression, then how is it that -(x+5)'must be positive?'

Hi,
As you have reached to x < -5, I will continue from this
x < -5. So, x+5 < 0 right?
So, (x+5) is negative implies -(x+5) is positive.

[Bens4vcobra]

If x < -5 from the given expression, then how is it that -(x+5)'must be positive?'

Hi,
As you have reached to x < -5, I will continue from this
x < -5. So, x+5 < 0 right?
So, (x+5) is negative implies -(x+5) is positive.

Thanks very much. I just figured out my error before I read your post. I had a "duh" moment. It was right in front of my face.

[Ozlemg]

Thank you. Great explanation...