Roland2rule wrote:What inequality represents the condition 1 < x < 9?
(A) |x|<3
(B) |x+5|<4
(C) |x-1|<9
(D) |-5+x|<4
(E) |3+x|<5
|x-y| = the DISTANCE between x and y
The midpoint between 1 and 9 = 5.
The given range implies that x can be any value between 1 (4 places to the LEFT of 5) and 9 (4 places to the RIGHT of 5).
In other words: the distance between x and 5 must be less than 4.
In math terms:
|x-5| < 4.
The expression in blue is the same as the following:
|-5+x| < 4.
The correct answer is
D.
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