corvinis wrote:
If |x| > 3, which of the following must be true?
I. x > 3
II. x^2 > 9
III. |x - 1| > 2
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
If |x| > 3, then it must be true that
EITHER x > 3 OR x < -3(1) x > 3This need not be true, since it's also possible that x < -3.
For example, x COULD equal -5
So, statement I need not be true.
ELIMINATE answer choice A, C and E
(2) x² > 9This means that EITHER x > 3 OR x < -3
Perfect - this matches our original conclusion that
EITHER x > 3 OR x < -3(3) |x-1| > 2Let's solve this further.
We get two cases:
case a) x - 1 > 2, which means x > 3 PERFECT
or
case b) x - 1 < -2, which means x < -1
Must it be true that x < -1?
YES.
We already learned that
EITHER x > 3 OR x < -3If
x < -3, then we can be certain that x < -1
For example, if I tell you that the temperature is less than -3 degrees Celsius, can we be certain that the temperature is less than -1 degrees? Yes.
So, statement 3 must also be true.
Answer: D
Cheers,
Brent
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