Is |x−5|>4?
(1) x^2−4>0
(2) x^2−1<0
OA B
please elaborate . Thanks in advance .[spoiler][/spoiler]
(1) x^2−4>0
(2) x^2−1<0
OA B
please elaborate . Thanks in advance .[spoiler][/spoiler]
}x-5| > 4?guerrero wrote:Is |x−5|>4?
(1) x^2−4>0
(2) x^2−1<0
OA B
please elaborate . Thanks in advance .[spoiler][/spoiler]
Case 1: x-5 > 4
x > 9.
Case 2: -(x-5) > 4
-x + 5 > 4
-x > -1
x < 1.
Thus:
|x-5| > 4 if x<1 or x>9.
Put another way:
|x-5| ≤ 4 if 1≤x≤9.
Question rephrased: Is 1≤x≤9?
Statement 1: x² > 4.
If x=3, then 1≤x≤9.
If x=10, then x>9.
INSUFFICIENT.
Statement 2: x² < 1.
No value between 1 and 9, inclusive, will work here.
Thus, it is not possible that 1≤x≤9.
SUFFICIENT.
The correct answer is B.
