Inequalities

I think it is B. statement III. Problem statement can be reduced to x<9.
St I can be x>5 which may or may not be true.
ST 2 can be reduced to x>-1 which again can be ambiguous, since a value of 10 satisfies II but not problems s
St III will always align with statement 1

The question stem is missing a set of parentheses.
It should read as follows:

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

• I.5<x
  2.|x+3|>2
  3.-(x+5) is positive.
  
  A.II only
  B.III only
  C.I and II only
  D.II and III only
  E.I,II and III

Simplify the expression in the question stem:
4 < (7-x)/3
12 < 7-x
x < -5.
Question stem rephrased:
If x < -5, which of the following must be true?

I: x > 5
Since x is negative, it is not possible that x>5.
Eliminate C and E, which include I.

II: |x+3| > 2.
|x-(-3)| > 2
|x-y| = the DISTANCE between x and y.
Thus, |x-(-3)| > 2 asks the following:
Is the distance between x and -3 greater than 2?
The question stem indicates that x < -5:
<--------(-5)......(-3).....
Since the distance between -5 and -3 is 2, and the entire range of x lies TO THE LEFT OF -5, the distance between x and -3 must be GREATER THAN 2.
Eliminate B, which does not include II.

III: -(x+5)>0
x+5 < 0
x < -5.
Eliminate A, which does not include III.

The correct answer is D.