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 implies the following:
The distance between x and -3 is greater than 2.
Plotted on a number line:
<-----(-5).....(-3).....(-1)
----->
The ranges in red are where x is more than 2 places from -3.
Since x<-5, it must be true that the distance between x and -3 will always 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.
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