karthikpandian19 wrote:Which of the following inequalities must be true for the value of x to be between -1 and 5?
A. |3 - x| < -3
B. -1< |x| < 5
C. |x| - 2 > 2
D. |2 + x| > 3
E. |x - 2| < 3
The correct answer must work for every value between -1 and 5.
Plug x=0 into each answer choice:
A. |3 - 0| < -3
3 < -3.
Doesn't work. Eliminate A.
B. -1< |0| < 5
-1 < 0 < 5
This works. Hold onto B.
C. |0| - 2 > 2
-2 > 2
Doesn't work. Eliminate C.
D. |2 + 0| > 3
2 > 3.
Doesn't work. Eliminate D.
E. |0 - 2| < 3
2 < 3.
This works. Hold onto E.
The correct answer should NOT work for any value NOT between -1 and 5.
Plug x = -2 into the remaining answer choices.
B: -1 < |-2| < 5
-1 < 2 < 5
Since x=-2 works in answer choice B, and x=-2 is NOT part of the given range, eliminate B.
The correct answer is
E.
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