|a| = the distance between a and 0.
|a-b| = the distance between a and b.
IF |X|>3, which of the following must be true?
A) X>3
B) X^2>9
c) |X-1|>2
I only
II only
I and II only
II and III only
I, II, and III
Constraint: |x| > 3
This means that the distance between x and 0 is greater than 3.
Any value in the two red ranges below satisfies this constraint:
<----(-3).......(3)
---->
I: x>3
The red range on the left illustrates that x does not have to be greater than 3.
Eliminate A, C, and E.
III: |x-1| > 2.
This statement implies that the distance between x and 1 must be greater than 2.
Every value in the red ranges above is more than 2 places away from 1.
Thus, statement III must be true.
Eliminate B.
The correct answer is
D.
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